They live in herds and have a very definite social order. To advance in the pecking order means a fight. If a bull is challenged and loses, he wanders away from the herd to live as a lone rogue. It is unwise to try to get too close to bison, and especially to feed or pet them. If you are seen as challenging the social order, you could be in for a fight you can't win, or outrun.
Bison are surprisingly fast and agile.
If you should ever find yourself close to bison, watch the tail. If the tail hangs down, the bison is content and does not feel challenged or in danger. But if you see the tail stand straight up, take it as a very serious danger sign. Quietly, but quickly, leave the area. The young bison breed at the age of three, and must be separated from their herd before then to prevent in breeding.