Why are Brahman crossbreeds commonly used for bull riding?

It's likely because they are easier to train for bucking than other breeds are. Brahman cattle tend to be considerably smarter than European cattle, and thus getting them to "get it" in the rodeo circuit will take less time than it would for a Charolais or Angus bull to be able to buck.

It's also probably because they look meaner than the other breeds do, and tend to have a more interesting variation in colour patterns which make them really easy to recognize from the stands and from a bull rider's point of view.