I have never stayed at All Stars resort so I can only give you an opinion based on what I have read about it.
Most of the posts I have read about AS resort and busing have been pretty positive.
That resort has a lot of rooms for a lot of people and I think that works in your favor.
I might think that your biggest challenge would be getting to and from water parks, animal kingdom & downtown disney.
Those areas seem to have the bigggest waits to, and definately FROM all the resorts!!
If I am sensing in you what I seem to feel is that when you are on time at a bus stop and the wait goes past the 20 minute window, you get cranky!!
I certainly do, we are spending too much money to have our precious vacation time stolen away from us!!
That is the only thing in WDW that MONEY CAN'T BUY, IS TIME!!
In that regard I would want a car for those places alone.
Now if you consider a potential for a problem to Magic Kingdom, Epcot or MGM on either the "to"or "return" trip a car seems a little more justifiable.
I'm not saying that you will have busing problems from AS resort but the potential is everywhere at all the resorts & parks. If you take the money for TTC and use it on a rental car and avoid just an hour a day of wait time on buses would it be something to consider?
Read these boards and get a feel for yourself about busing, if you already haven't.
Good Luck!!
p. s. If you don't get a car don't worry about your stroller, just fold it up and get on the bus, everyone does!
