Zimbabwean wanting to go to the U.S.

I have Indefinite Leave to Remain in the UK but still have a zimbabwean passport, my band are doing a month long tour in the U.S., has anyone got any idea of what getting a visa will involve?

http://www.usembassy.org.uk/cons_new/visa/index.html

You should really think about swapping your Zimbabwe passport for a British one. I have come across numerous cases where people living outside Zimbabwe are being denied passport renewal and are effectively stateless once their passports expire, or if the passport is lost or stolen.

If that were to happen outside the U.K. you might struggle to get readmitted because you would have no travel documents.

The Americans are probably aware of the problems with the Zimbabwe passport and may be reluctant to put a visa in one.