You define places where only one person is allowed at a time, a camera records the entrance to the place. If someone reports being attacked at given place, and the accused student says "actually,
he attacked
me", then you look at the record. The person who entered the place
second is the one who broke the rules. Plus, you know he is lying to you.
The problem with bullying is not just that someone can beat you up, but that if you try to complain, the bully can say "actually, he attacked me" or "no, we were just playing" or something like that, and the teacher will be like "wtf, I have no idea what actually happened, so just shake hands and be friends again, okay?" And you know you get beaten up tomorrow again. What an improvement it would be to have a place where, if you get beaten up, at least the camera will record that you were the victim.