n=1 anecdote, but my experience is that I had equally-bad (if not worse) bullying experiences outside of school than inside.
What I suspect is happening is that the school environment mixes people of different "cultures" much more thoroughly than non-school environments, which greatly increases the possible exposure of would-be bullies and would-be bully targets.
The other obvious thing that comes to mind w.r.t. school and bullying is that one fallback option for dealing with bullying is leaving the situation, but in school, if you want to switch classes or even schools to avoid a bully, I think you would basically have to ask some adults for permission, and if they don't grant it, tough luck--you're still forced to spend N hours per weekday there. Non-school activities seem less likely to be so compulsory (though if the activity is "walking in your neighborhood and encountering your bully", complete avoidance would require moving), which would seem to put some upper limit on how bad a case of ongoing bullying can get.
Could you comment on how the above relates to your experience?
In middle school (the only time when I had any sort of bullying problem at school), the problems all stemmed from gym class. The school system had decided to send both the GT and the emotionally-disturbed students to the same school, but the only place where the two groups ended up mixing was gym class. Well, maybe some elective courses as well, but I never had any problems there.
I think that the bullying only really ended up happening (both in and out of school) when there was no adult supervision. I'm not entirely certain, though, since I have tried to purge my memories of what happened during those times.
What I suspect is happening is that the school environment mixes people of different "cultures" much more thoroughly than non-school environments, which greatly increases the possible exposure of would-be bullies and would-be bully targets.