I like the idea of having friendships that Bully1337 mentioned above, say there is some kind of friendship meter that everyone has, kind of like how there is in the Sims?
You guys have introduced some great ideas for the next Bully, I'm not too sure if I'd like to see the game set in Bullworth again, or have it move to an entirely new fictional town in America. In all honesty I would be happy with whatever way Rockstar decides to go on the story and location. Perhaps in a scenario where Jimmy has since been expelled from Bullworth Academy after the events of the first game. His mother has since gotten divorced and has met some new rich old guy and is once off again to get married and go on a year-long honeymoon.
I would like to see the new town much bigger, perhaps it could be divided up into four different districts (each being the size of the map in Bully or even bigger) and each housing it's own unique school. (public school, private rich school, community college, army college) Each school would have it's own new cliques.
I really enjoyed reading Bullyfan No.1's ideas for the new cliques that could be added into the game, I will also add to that there should be hipsters, goths/punks, skanks/sluts, and also the wannabee gangsters lol.