I don't think it has much to do with class, to be honest. Here in Toronto, there are a lot more indians and asians than there are blacks and any woman, regardless of class, would have plenty of exposure to these groups. Yet, you rarely see white women dating them. I think it has more to do with the fact that asians and indians in North America are perceived, rightly or wrongly, as nerdy, shy and "funny", which is obviously seen as a negative by most women.
On a side note, I honestly don't see why minority men are so desperate to date white women in the first place. Does your status in your community go up if you date a white woman or something? As a minority in an interracial relationship, you will never be able to control the frame because of your lower perceived social ranking.