Small amounts of Al in bronzes give it lots of strength and wear resistance (Al/Ni bronze e.g.). Generally, the aluminum will form a very tightly adhered oxide layer on the surface of the bronze, lending some passivity. You'd need an awful lot of Al for it to form a flaky white layer.
Lead oxide is white (thus its use in "lead paint"). Lead in cast bronze doesn't alloy with the parent copper, but exists as a seperate phase (this helps form chips during machining, also the lead lubricates the cutting tool). Because it isn't alloyed, the lead near the surface of a cast part oxidizes out pretty quickly, and can coat the surface of a wetted then dried part.
Zinc oxide is white too (think diaper rash ointment, or at the beach on a lifeguard's nose). Zinc, in the presence of chlorinated water or hot water, will leach out of some brasses and oxidize if no tin or arsenic is present. You said you have a bronze, which typically includes tin, so this is probably not the problem.
The green color on oxidized bronze/brass/copper comes from copper corrosion salts (chlorides, sulfates, etc., which can happen when the corrosion occurs in a slightly acid environment with those contaminants present). Red copper oxide is a pretty tightly adhered layer on the copper.