Well I think you have an advantage over those who exclusively play the lighter strings of an electric guitar, because the first thing that you'll need to get used to is the heavier gauge of the bass string. The bad news is that your fingers will need to be even stronger to hold down that heavy low E...but the good news is that if you've been playing acoustic guitar for awhile you've already gone through the pain of building up calluses on your fretting fingers, and the bass strings aren't as painful as the acoustic strings...they don't cut into your fingers quite as much.

Musically, though, it is quite a transition to go from any kind of 6-string guitar to the bass guitar. I look at the bass as an extension of the rhythm section...its role is a lot different than that of a guitar. While rhythm guitar needs to groove with the drums, too, the bass is the all-important glue that connects the melodic stuff (guitar/keys/vox) and the rhythm stuff (drums).

So it might take awhile to get a feel for that different approach, but it's totally do-able. I was a guitar player-turned-bassist for a couple years in a couple different bands before I really "got it" and started to concentrate on just locking with the drums and only contributing cool bass lines when appropriate for the song.

I'd suggest starting to play with your fingers (i.e. plucking rather than using a pick) first and then you can always go back to the more comfortable pick usage later. This will really force you to feel the groove and it'll kind of help you separate the role of the bass from the role of the acoustic guitar in your mind, I think.

Good luck with it!