We stayed at the BC in May and did not have a car. Transportation was not a problem at all. I don't think we waited more than 10 min for any bus. Being able to walk to Epcot is a great asset. We never waited more than 10 min for the boat to MGM either. We did take a taxi a couple of times, because we didn't want to chance making our PSs. Taxi was no more than $11 any time we used one. If I were to stay at the BC again (which I'm sure I will my 3DSs absolutely loved it there) I wouldn't bother to rent a car next time either.
Have a great trip.