Right, they get the bar that shows their relationship to you. Bullies can get a dominance bar from bullying you. I think it contributes to the hatefuck relationship but I'm not entirely sure.
Technically you CAN get the bully inclination, but I don't think there's a lot of use for it so far, sadly. You can get it by choosing to trip people when randomly prompted for it when leaving class, or you can cheat to get it.
So far the only really 'mean' actions I've noticed is joining in when a bully is messing with someone, throwing paper back at bullies, tripping people, or gossiping about your rival to other students when you sit to eat with them.