Even though Bully doesn't exactly promote violence, it certainly doesn't shy away from putting people in their place. Combat is simple, beginning with nothing more than square-square-square types of attacks, but eventually you can hit circle to "finish" the other guy off with a humiliation move. What kinds of moves might these be? The "stop hitting yourself" face slap and Indian burn should give you a good idea.
The catch to roughing kids up is that teachers and prefects can bust you hard for violence - if you even attempt to pick on a girl or little kid, you're done. Should you fail to escape, you're taken to the principal's office, where a punishment is handed down. And yes, you actually have to fulfill whatever they tag you with, be it mowing grass or shoveling snow. The lesson here is obvious: just like in real school, only pick fights you can blame on someone else.