The BAII allen wrenches are so tiny that they don't usually come with most standard wrench sets, I have a few sets here and the only way I could adjust my BAII was with the wrench that came with it. Don't know the size though, sorry.
It's a SAE 0.05" allen wrench for the BAII bridge saddles.
You can order the single wrenches online, or I found it as part of a set at a Lowe's. A lot of allen wrench sets (including several that I already owned) stop at 1/16", which is the next size up from the 0.05".