The other thing I know is that most of the adults -- particularly those in charge of schools -- are utterly feckless at stopping bullying, and all the rallies and posters and nanny-talk just function as a big bandage over the festering wounds. In order to stop bad behavior (including bullying), every adult must be empowered to stop it and administer consequences, and there must be an adult within observation distance of the vast majority of interchanges between kids. Tn more intimate settings such as church or scouts, we have this. I can make my displeasure known immediately to someone who acts inappropriately without being smothering; schools are so structured that the adults float above the seething mass of students, unable to quickly and effectively reach into the mass of kids and call down the ones who are misbehaving.
Now, it may not seem possible to be within observation distance of the vast majority of interchanges between kids, if we're talking about playgrounds, neighborhoods, and so on. But when we're talking about unstructured activity out in the wide world, it's fairly easy to avoid bullies and other buttheads. The worst bullying happens in places where people are required to be with others en masse -- schools (and prisons). Your kid can't self-select out; meanwhile, the mass conscription which is public school is a bonus buffet for bullies, who have greater opportunities to torment others because those others are required to be in the same building as themselves and the adults largely leave them to it. In the absence (nay, abdication) of authority, the law of the jungle asserts itself.