I think yes a white guy or Asian guy for that matter CAN chase a bucket of chicken, but a black guy is far highly more likely to do it and not think twice. A white guy would rather have a steak or hamburger, an Asian guy would chase sushi or dim sum. In fact, I would chase sushi and dim sum if it was in a bucket just sitting there. But a black guy (Bush is black by the way), he is going to chase a bucket of chicken 10 out of 10 times.
So in this event, Bradshaw knew what he was saying, and yeah it has some racial bias, but this guy is an idiot and will say anything for a rise! I think most people are sensitive to comments like this, so its not racist or slandering at all, but it hits harder with the black population as they seem to be more sensitive.