Tough problem, because it is usually so hidden. When I was bullied, the very last thing I wanted to do was draw attention to myself, so of course I never told anyone about it. I never believed school authorities would do anything, or could do anything to help. Reporting to them would just make me a bigger target. I suspect this is normal.
The bullying did eventually stop, but it was because of things I did. I joined a sports team, and that alone stopped most of it. A few times I got mad and told off the person trying to push me around, and that helped too. I was fortunate that it was verbal bullying, threats, not actual physical bullying, and I doubt I was ever in real danger.
So my prescriptions are: One: School staff has to make it clear that they will support bullied kids. That means that there have to be real and clear consequences to the bullies. I honestly doubt this will ever happen on a wide basis. Bullies are usually the popular kids, the ones the teachers like. Bullied kids are often the slow, stupid, un-athletic kids, the ones who the teachers don't notice or care much about.
Two: Bullied kids have to be taught how to handle it. They should be encouraged to become stronger, more confident people. They should join a sport, or a popular club, as that helps make them insiders, not outsiders. The sport I joined was the same one that had my bullies in it. By joining, they no longer saw me as a target. Obviously, this isn't going to work in many cases. I was lucky that my bullies were not really all that bad, although I thought so at the time.