I don't have kids, so take this for what it's worth.
Kids are mean little jerks, for multiple reasons. (Obviously I was bullied, with this attitude, but I understand now that I freaked my classmates out by being on the autism spectrum, having a ginormous vocabulary (frequently got made fun of for using big words), and best of all for them, was chubby.)
I can't even imagine what it's like now with social media.
But back to my point--I'm not sure there's a way to stop kids from being mean little jerks, and they can't be watched at all times. They're working out their own home or ego issues, they're figuring out how the social pecking order works (or sometimes they're just plain mean). So there's no way to fix that ... I don't think? Any more than they can be stopped from experimenting with things their parents would rather they didn't, if they get it in their heads to do so.
And in my specific bullying experience, even if a teacher or parent did intervene, I just got it worse the next day.
It feels like the answer is to somehow convince the bullied child to care less about what the other kids think. I know confidence and ego is incredibly fragile at that point, and that it's difficult to convince a kid or teen that the situation is temporary. But I feel like if it was my child I would be doing my best to convince him or her to laugh off the stupid shenanigans of their classmates, and that ignoring them would be the best revenge.
I'm sure this is all easy for me to say as a non-parent. I just, sadly, don't see a way to fix the inherent meanness of kids (and they have so MANY ways and opportunities to bully now), so teaching the bullied kids coping skills and self-respect as hard as you can would be the only thing I'd feel like I had any control over. (I'd also teach them the finer points of freezing people out and/or the art of the sarcastic comeback.)
Again, I am definitely under qualified for this, just thinking out loud about a problem that seems like it has no solution.