For what it's worth, we teach one or more kids to ride virtually every week, usng our own balance bikes or, for taller kids, the tried and trusted pedals off their own bike method.

I can't speak to the Balance Buddy, but since many of our kids are 3 years old we're in the same position as you, re height. One thing we never do is hold the bike. We simply place a hand, often fingertips only, on the upper back. We find that this provides just enough control to give the learner confidence that they're not gong to be allowed to fall and then they're away. Even with a very light hold on the bike, there's a danger of the bike going where you're pushing it which may not be [I]quite[I] where they're steering it.
As for "training" wheels, they are an abomination and should be made illegal, since they don't train kids to ride. Good luck, whatever you do.