You're slightly out of luck; due to the FAA ruling mentioned above, no oxygen tanks are allowed to be used onboard commercial flights, and must be sent as cargo. Also, Virgin America explicitly disallows passengers who require breathing assistance from flying with them, and recommends that alternative airlines be used instead. There are some airlines who make allowance for the use of portable oxygen concentrators though. Given the departing airports that you have mentioned, the following airlines can provide inflight oxygen using portable oxgygen concentrators, for a fee.

AIR FRANCE (IAD, cost not stated)
AMERICAN AIRLINES (BWI & IAD, $100)
CONTINENTAL AIRLINES (BWI & IAD, cost not stated)
COPA AIR (IAD, $75)
DELTA AIRLINES (BWI & IAD, $100)
NORTHWEST AIRLINES (BWI & IAD, cost not stated)
UNITED AIRLINES (BWI & IAD, $125)

The above airlines underscore the following terms and conditions:
1) The provision of oxygen is made available only while your mother is onboard the aircraft.
2) You will have to get your mother's physician to sign a release form
which you must have available at all times, confirming your mother's
request for oxygen, as well as the required oxygen flow rate in liters
per minute (LPM)
3) Advance notification of your requirements is needed at least 48
hours before the flight itself, but preferably as ahead of time as
possible.

I'm looking at your question again. To use a looser definition of "accommodate", the following airlines are also worth mentioning:

AIRTRAN (BWI & IAD)
JET BLUE (IAD)
US AIRWAYS (BWI & IAD)

These airlines do not provide passengers with their own in-flight oxygen, but will allow the use of passenger-owned portable oxygen concentrators. Depending on your needs, you may want to consider using a portable oxygen concentrator rental service called Oxygen To Go: http://oxygentogo.com

Many airlines do allow the use of oxygen concentrators during all phases of flight, including take-off and landing. The FAA passed a law in 2005 I believe that allowed airlines to do this(but did not require them to). It's best to check in with your preferred airline and ask them about their medical assistance and procedures for using medical oxygen.

For Virgin Airlines, check here:
http://www.virgin-atlantic.com/en/gb/passengerinformation/inflighthealth/medicalfacilities.jsp

If you need to know anything else for medical oxygen as it relates to flying, check the other sources below, or contact me directly. Hope this helps!

Currently the following airlines allow the use of the travel oxygen concentrators onboard their aircraft ( Virgin atlantic airways is also listed here)
There are various formalities to be taken care before you board. The following website features all the necessary details.

If the airline you are flying isn't listed or doesn't contain a link, call us for information, Toll-Free 866-766 5247.

the above info was taken from
--------------------------------------

http://www.oxygenfreedom.com/travel_oxygen_information.html

All airlines accommodate use of oxygen tanks while traveling. But, you need to do some "ADVANCE PLANNING".

1. Your trip begins with the airline. Each airline has its own policy for on-board oxygen transport and in-flight oxygen usage. You will need to contact the individual airline for their current policies regarding oxygen.

2. You must carry your prescription for oxygen with you at all times. Many of the airlines have their own airline specific medical form for your Doctor to fill out. These are generally good for one year. A helpful tip: keep your other medications, prescriptions and forms with you while traveling and not in your checked baggage.

3. The FAA has approved several POCs (Portable Oxygen Concentrators) for in-flight use for passengers requiring oxygen - the Inogen One, AirSep Lifestyle, AirSep Freestyle, SeQual Eclipse and Respironics EverGo.. These are the only POCs approved at this time. (Airline Oxygen) They can be stowed under the seat in front of you during flight and can be battery powered when not plugged into an electrical socket. Remember: YOU must confirm with your airline carrier that they will allow your POC on your specific flight.

NOTE: YOU ARE NOT ALLOWED TO USE ANY OTHER PERSONAL OXYGEN SYSTEMS ON BOARD. FILLED OXYGEN TANKS (LIQUID OR COMPRESSED GAS) CANNOT BE CHECKED AS BAGGAGE ON ANY AIRLINE. While a few airlines continue to provide oxygen for their traveling passengers, most do not. Some airlines will allow empty oxygen equipment to be stowed in baggage but it must be verified as empty and the regulator removed. Check with your airline ahead of time to see if they will allow empty systems/tanks as stowed or checked baggage.

4. Once you have decided on your oxygen needs, you will need to contact your oxygen provider to see if they can provide you with a POC approved for air travel. If not, you will have to rent or purchase one independently. (POC Information) You will need sufficient battery power to cover pre-flight, in-flight and post-flight time. Remember you will need to arrive at the airport 1 – 2 hours ahead of your flight time. At Gate Check-in you must have battery power for at least 50% longer than your scheduled flying time. (For example – if your flying time is 3 hours, you will need 4 ½ hours of battery power) You will need to cover your travel time to the airport, airport waiting time, your flight time and the time it will take you to deplane, pick up your checked baggage and travel to your final destination. Plan ahead for any possible delays. Non-Stop or direct flights will keep the battery time to a minimum.

5. The Department of Transportation (DOT) provides public tips on safe carriage of batteries and battery-powered devices such as medical equipment. For information on how to safely travel with oxygen equipment batteries, please visit the DOT web site.

6. You may want to contact your insurance carrier to determine coverage for your oxygen needs while traveling.

7. When you make your flight reservations be sure to advise your airline you intend to travel with oxygen. Most airlines require that you contact them at least 48 hours before the flight to advise them that you will be traveling with oxygen and the form of oxygen with which you will be traveling.

8. At the Airport you will need to pass through Airport Security. If you are traveling with an approved POC, that will need to be identified on the POC itself. All TSA approved oxygen systems can safely be x-rayed if requested. If you are traveling with a portable oxygen system, you will be allowed through the security area after inspection and may take the system to the gate. If the system is not an approved POC you may NOT be permitted to take it onto the airplane and will need someone with you to remove it from the airport. If you do not use an approved POC oxygen supply you will need to arrange for an oxygen supply at your destination.

Have you considered the train?

Amtrak fares look like they're around $195 each way between DC and LA.

The big difference of course is the amount of time. But taking a train can be relaxing and even a fun way to see the country.

It may also be nice for your mother to be able to stretch out or get up and walk around since she's on constant oxygen.

Without the long security lines, generally stressful travel, etc a lot of older folks enjoy the train a lot more than airlines.

Your won't be able to carry your own tanks onboard, but many airlines provide oxygen to it's passengers or at least Portable Oxygen Concentrators. In any case, you will want to give the airline plenty of notice of the needs, and see what options and even fees they have for this service.

http://www.continental.com/web/en-US/content/travel/specialneeds/disabilities/oxygen.aspx
"The Federal Aviation Administration (FAA) requires oxygen on airplanes be dispensed only from FAA approved containers available through the airlines. Specific certification must be obtained by Continental that mandates the type of container utilized. All requests and reservations for this service are handled through the Oxygen Desk. Customers in the U.S. can contact the Oxygen Desk directly at 800.228.2744. Customers outside of the U.S. should contact Reservations. There is a charge for this service."
http://www.usairways.com/awa/Content/international/en-UK/travel_information/special_needs/medical.aspx
"Guidelines and restrictions
Effective November 2, 2005:
Passengers who require medical oxygen may travel with approved portable oxygen concentrators (POCs). US Airways approved POCs are: Inogen One and Airsep Lifestyle models. These devices are permitted for use on any US Airways, US Airways Shuttle or US Airways Express flight (except for Beechcraft 1900 aircraft). You must be capable of hearing alarms and seeing alarm light indicators and taking appropriate action in response.

For codeshare flights, contact the operating carrier for rules on traveling with portable oxygen concentrators on other carriers.

* Unit and battery supply are not counted toward free carry-on baggage allowance. Batteries must be packed individually to prevent short-circuiting and damage.
* Ensure that the unit is free of oil, grease or other petroleum products and is in good condition free from damage or other signs of excessive wear or abuse.
* Inform the gate agent that you intend to use a portable oxygen concentrator on board the aircraft.
* Carry an adequate battery supply with you in your carry-on luggage. "

Virgin Atlantic- They provide therapeutic oxygen onboard
http://www.virgin-atlantic.com/en/us/passengerinformation/inflighthealth/medicalfacilities.jsp
"Therapeutic oxygen is available onboard but please contact Special Assistance to confirm whether these arrangements can be made. We require as much notice as possible."

BMI - Provides Oxygen bottle for fee
http://www.flybmi.com/bmi/en-us/flight-and-airport-info/pre-travel/special-assistance/special-assistance.aspx
"If you need additional oxygen onboard the aircraft, then, for a fee, we can provide this service. Only bmi supplied oxygen bottles may be used onboard our aircraft. We'll require you to complete a medical form to help us plan for your needs throughout the journey. Call us on 1 800 788 0555 to find out more."

Continental - Provides oxygen
http://www.continental.com/web/en-US/content/travel/specialneeds/disabilities/oxygen.aspx
"Continental provides limited onboard medical oxygen throughout our domestic system, including Alaska and Hawaii. We recommend your travel plans be confirmed as far in advance as possible. All travel must be approved by your personal physician. A minimum of forty-eight hour (48) advance notice request must be made so we can guarantee shipment of the appropriate medical oxygen canisters to your origination point."

US Airways - Allows you to bring your own Portable Oxygen Concentrator, but not bottles
http://www.usairways.com/awa/Content/international/en-UK/travel_information/special_needs/medical.aspx
"Provide a medical authorization form or doctor’s statement to the flight attendant once on board the aircraft. The form will be returned to you. Your POC must fit underneath the seat in front of you or in an overhead bin. You may not be seated in an exit row."

You can rent a compliant POC here:
http://oxygentogo.com/entry

Virgin Blue - Requires you provide your own oxygen via POC
http://www.virginblue.com.au/Personal/Flightinfo/SpecialNeedsandAssistance/Medicalconditions/index.htm
"If you require supplementary oxygen or use a portable oxygen concentrator in-flight you must make your booking through our Guest Contact Centre (internet discount fare will be honoured) as restrictions apply. You must supply your own oxygen or concentrator from selected suppliers."

United - Oxygen via POC provided in flight. Other arrangements must be made during ground time.
http://www.united.com/page/article/0,6722,1043,00.html
"United provides in-flight oxygen only. If you require oxygen during ground connections, please contact an oxygen vendor or refer to the information below regarding portable oxygen concentrators (POC). We suggest you work with your physician to determine the most appropriate arrangements."

Arranging for Supplemental Oxygen (O2) Aboard the Aircraft

* Neither the Air Carrier Access Act nor the Americans with Disabilities Act require airlines to provide oxygen service. Consequently, airline policies, procedures and services on accommodating passengers who use supplemental oxygen vary widely.

* Notify the carrier when you make your reservation that you will need to use supplemental oxygen aboard the aircraft(s).
* Ask about the airline's policies on the use of supplemental O² onboard. Federal regulations prohibit airlines from allowing passengers to bring their own oxygen canisters aboard to use during the flight. Passengers who use oxygen canisters must purchase canisters from the airline for use during the flight. However, some airlines do permit passengers to bring aboard oxygen concentrators, which do not contain oxygen, and use them during the flight. Policies vary from carrier to carrier, so be sure to check with your airline well in advance.
* Keep in mind that not all airlines offer supplemental oxygen service, or may not offer it aboard all their aircraft. Inquire whether: 1) the airline provides oxygen service, 2) it is available on the flights you wish to take, and 3) you must provide a doctor's letter, or permit them to contact your doctor directly to verify your medical need.

Websites for each arline have information on their individual oxygen policies. I would carefully evaluate the information on the airline sites that service your destination.