Hi Michelle,
First off, your question about the chances of getting a last minute reservation at BBB-MK from a cancellation...... it is possible, we managed this on our last trip.......but it's not likely. It was a total fluke for us and we happened to be right there when someone called to cancel an appointment ten minutes before hand. It was so random. Everyone wants an appointment there, and everyone is constantly checking for those last minute spots. It could happen for you but I would never count on it.
Secondly, your current appointment at BBB-DTD at 1:30....... if you must rely on the buses I can see it possible that you'd arrive on Main Street as late as 4:30. With MK closing at 7:00 on your day, this really wouldn't be worth it. It is possible that you'd get there a bit earlier IF your daughter's appointment starts exactly on time, IF all decisions about hair, costume etc are concrete ahead of time, IF the bus is waiting for you when you're ready to go, IF the security check and entry lines at MK aren't backed up, IF no one needs a break for the bathroom or water or a snack.
That's a lot of IFs. If it were me, I'd considering skipping the BBB. Yes, it's fun and it's special but your child is already going to be blown away by this surprise trip. Maybe avoiding a stressful, rushed situation in favor of having a full morning and afternoon to just enjoy Magic Kingdom is a better way to go? On a first trip there is soooo much to see and do. Your daughter is going to have a great birthday just by being there.