Many of the brass browning products will work on bronze.

It's called "patinating" (putting a patina on metal). There are various forumlas that can be utilized, and each gives a slightly (or very) different aged-broze effect. Often the metal must be heated first so that the moisture is driven out of the microscopic pores of the metal and so that the patinating chemical can penetrate and do its work. But all in all, the patinating process isn't a really difficult feat.

See if you can find - possibly through inter-library loan - a book titled Patinas for Silicon Bronze. It's the complete guide to getting the effect you want.

Best of luck with it.