Maybe the problem is not related to size of the school but only related to the fact that kids have no choice in going there?

In the adult world, in most cases you aren't forced to go anywhere and only do so because you have a good reason, whether it's the workplace (earning money), universities (learning things because you need that knowledge), etc. Most people go into an establishment with a goal in mind, work towards that goal and have little time nor motivation for things like bullying.

School is different because kids have no say in the matter, so even if they aren't interested in learning (because the coursework is boring, irrelevant, etc) have to go there and waste ~8 hours a day and need to occupy themselves. Typical sources of entertainment (television, video games, etc) are forbidden so bullying, or similar anti-social activities happens to fill the gap. This results in a lose-lose situation; kids that aren't interested in the coursework are having a miserable time and entertain themselves by making the environment miserable for everyone else (both other pupils as well as the school staff).

For a year of middle school and a couple years in high school, I went to a "distinguished" secular private prep school in Oklahoma City. I think there were 60 to 80 students per grade, with small class sizes, much smaller than public schools. And let me tell you, there was plenty of bullying there. It was endemic.

One of my regrets is that I didn't just drop out of high school at 15 and get my GED. I took the ACT test twice, once at 15 and once at 18, and there wasn't really a difference in my score. I suppose the one real difference is that the second time, I had fewer fucks to give, and a buddy smoked a joint with me before I took the test.

The only institutions in life that I know of where you are forced to attend and prohibited from leaving on your own recognizance are school, prison, and a mental health facility to which one is involuntarily committed. Perhaps nursing homes are another.

That said, I have a lot of respect for the teaching profession. I had some truly incredible teachers.

I doubt that a larger school has more bullying per student. In large schools the students tend to subdivide into non-intersecting groups (e.g. nerds, jocks, rednecks, punks, etc). I went to a medium/largish high school and there were kids in my graduating class that I had never met, did not know their name, etc. Kids in these differnt groups largely left each other alone, because they did not compete for the any of the same things. Fights were usually between members of the same group.

I suspect you may be right that even ~400 or ~500 students is too many.

This is just an anecdote. I went from an enriched program with a high school of about 500 students, which was quite wonderful, but still had the usual high school social issues, to another enrichment school of about 60 students. It was socially different. Everyone knew everyone well. You had to get along.