I never liked wearing bras when I had to start wearing them, and even now, at 18, I can't stand wearing the "normal" kinds, with the clips or the wires because they irritate my skin (I wear sports bras). I remember being about 11 or 12 and pushing my bra up onto my upper chest just so I wouldn't need to feel them pressing against my breasts. Hey I was still wearing them...but no one said I had to wear them properly, right?
I'm also going to venture a guess that, once people start making comments to her about bouncing around, she might decide that she wants to "limit her freedom", so to speak. I say to just give it time. With young girls who choose to abstain from bras, sometimes the only way to prompt them to wear a bra is to let themselves get embarrassed when they don't wear one and people start making remarks behind their backs. Don't worry about it a whole lot - one day, your daughter will come up to you and ask when she can go bra shopping again.
Has she tried those tanktops with the built-in bras? Or don't they have bras now that are just cups (with some kind of adhesive tape)? If all else fails, your daughter can always stretch a piece of duct tape across her chest.