I don't see a problem with "bit". The only objection I've seen is that it could be confused with informational bits, but those very rarely come up in the same context. British use pound for both currency and weight, and that doesn't seem to be a problem. I think bits is a very marketable name with a real chance to catch on.
mBTC and uBTC are very easy to understand. Or do you think people using Bitcoin dont have idea what SI unit prefixes are ?