I love bronze (I buy mine from Rio) and tend to use a brass brush while I’m working on my project. Bezels, soldering to back plates, that sort of thing. Toward the end, or where it seems necessary, I’ll use the “super pickle” that Eileen mentioned.
It’s easy – just dipper out enough regular pickle to cover your piece, then add the hydrogen peroxide. Put your piece in and watch the bubbles. When they are gone, your piece should be clean.
Note that the hydrogen peroxide is spent within an hour or so of mixing it in with the regular pickle, so there’s no sense in keeping the mixture around. It just turns back into regular pickle (+ the water that the hydrogen peroxide has reverted to).
If your regular pickle is already warm, then a beaker or glass jar should be fine for the temporary super pickle.
This is all based on my experience with Rio’s bronze (copper + tin), so another bronze alloy might act differently.
Good luck! It’s such a beautiful metal.
Edited to add: I forgot to mention that the proportions are 1:1 (one part regular pickle and one part hydrogen peroxide). I don’t think it’s critical to be super-accurate with the mix, so anything close should work. Note that I’m not a chemist, though.