If Dominance appears it means they are dominating you, while Submission would mean you're the dominant part in the relationship, right? I've seen the dominant bar appearing in bullies/rival relationships and it was a bit confusing
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.