I think mine were bouncing and such after about four months? I don't know when they would have needed a bra, since I was wearing one before HRT (I was out full-time several months before I could afford doctor appointments and 'mones)... Anyway, these kinds of things differ so much from person to person. Some grow faster, some grow slower, some grow bigger, some grow smaller. It's the same with cis women when they go through puberty.
As for trying to maintain boy mode with boobs, you could probably get away with a sports bra unless they get really big. Then, you'd probably want a binder if you're trying to pass as male.