balance bikes are massively popular here - my dd hated hers, but ds 2 loves it.DD would not ride a bike at all, a friend of mine tried to force her once - that went very bad. We started going to a hbike park with a playground attached, DD eventually asked for her pedal bike and rode no problems. She just didn't like feeling like she didn't know what she was doing. Watching other kids ride helped her get the idea.
Also maybe a scooter is a better idea. I know in our area most kids have a scooter, but bigger kids tend not to have bikes as there aren't many places safe to ride them right now. I'd be surprised if your DC was the only one with a scooter at bring a bike day. Maybe chat to the teacher.
