Bullying is a problem in many schools. One solution I have to this problem is to install surveillance cameras all over the school. The school can employ a security guy to watch the school with these surveillance cameras, responding to any cases of bullying as they happen. Another idea is to have some sort of software that is able to recognize when a fight begins and then warn security about it. Facial recognition software exists, so I don't see why fight recognition software can't exist.
Of course, bullying can be about so much more than fighting. E.g. it can be about verbal abuse, e.g. calling a child ugly or fat.