A college setting would be way more interesting. I think the thing that makes the most sense is a fictional college town with a giant, run of the mill university and a smaller, prestigious one. Some of the conflict in the story could come from the tension between the two schools once the player resolves conflicts at their own college (the giant one).
For some reason, Texas seems like it would be the best setting. It's a pretty unique environment and could allow them to get crazy with characters and environments. A smaller setting (a small college town and the surrounding rural area) would also allow them to go more in-depth. Rather than a massive open-world, you're getting a small, but remarkably dense one.
The missions would all be smaller in scope. It should feel believable in a college setting.
The three character configuration from GTA V should make it's return. While I thought it was a bit goofy in GTA, because the characters were so similar (all are criminal men), it could shine in a Bully sequel. A nerdy freshman guy, a popular upperclassman girl, and an eccentric, old Professor could be really awesome and give Rockstar a ton of options when it comes to crafting missions and story-lines.
I think a big part of the game would be social links. Expanded dialogue options, romantic interests (flirting, relationships, sex, multiple partners, infidelity, etc.), and increasing your social standing to access new areas and missions would be really fun.
Another big part of gameplay would be time management. Go to class and study to keep your grades up, hang out with friends to build relationships, meet your basic needs (laundry, sleep, and food). Obviously, all of this would be super lenient, but always having it in the back of your mind would be interesting. You can stay at any point in the year by not doing story missions that would advance the school year. The entire game would take place over a single school year and would be designed with replayablility in mind to join different social groups, build different relationships, and experience different things.
The narrative could be based on different college events throughout the year, with the characters weaving in and out of each other's lives (although not necessarily in as obvious of ways as GTA V). The game would be light-hearted in tone, but careful not to tread into the GTA-style satire. To some degree, I'd like the game to take itself seriously, even if it is comedic and light-hearted in tone.
The gameplay would be focused on more social interactions, but would include stealth, driving, melee combat, and even some shooting elements.
