When you say "Asia", are you using the American version of the term, which is basically the Pacific Rim countries and China? Or the European "Asia" which includes India? My question really is whether Bollywood is as "black-averse" as the Pacific Asian market is...
India has its own problem with race: for example The issue of Indian actors and actresses being photoshopped so their skin tone appears lighter in magazines/on covers, etc, is a significant one in India/Bollywood, or that's my understanding, at least.
India is largely an indigenous market. You're generally safe assuming that the Pacific Rim will watch whatever the Chinese like. Bollywood produces plenty of content for India; the stuff they buy from the US is generally things that are big and expensive and full of explosions.