Bullying is highly correlated with environments that are strongly hierarchical and authoritarian. What is a compulsory school but an authoritarian and punitive environment where everyone is ranked and some people have more power than others? The bullies are simply emulating the system around them!
Yet there are solutions. Bullying experts go into schools to suggest ways to reduce bullying. They talk about more respect, less punitive pressures, and less emphasis on ranking, among other things. In short, they tell them to be more like Sudbury schools.