You didn't say what sort of bra size you normally take, but here's a punt at some bras I've worn in the past and have been fairly comfortable on the bicycle.
I've used:
Ultrasport, made by Bras N Things - this one I found to be very caging. You'll have to wear a t-shirt with it because the straps are so wide they'll be visible otherwise.
Sports bras by Berlei - they make a variety, including a type of the one above, and other non-wired ones.
Sports bras by Triumph - are labelled by how supportive they are, although they don't have this on the website, weirdly. If you see them instore, however, they'll have "support factor 2" up to "support factor 5" (this latter being the highest).
Target also makes knockoff bras of Triumph and Berlei which are pretty good, and about ten dollars or so cheaper. I've been buying theirs a lot except for when I get to strange bra sizes; when 10DD or 10D it's hard to find bras at the right size there, and so it's off to the bra shop I go. I don't know what styles I have anymore because of the tag printing being washed off with repeated washings. I've tried almost every type, though.
Go to a bra shop and to the sports section. Good sports bras are expensive--unless you go to Target, that is--and are highly fugly. The less ugly they look the less support they provide, so those that look like you had a paint splatter on your chest and there's more fabric than skin showing: those will provide the best support! Just know you can't wear a pretty lowcut top with them. And they'll set you back $40-80, depending on your size. Try them on, with the help of a salesperson maybe (unless they find they don't have the particular size of yours in stock and then they're all "well, if you adjust the straps this way, it will fit just as well as the other size"--just say no). Jump up and down a lot and figure out how much bounce you're getting.
Good luck!
