I don't know if this is sure-fire, but here's what I do:
- Find-out what clique the bullied person is in. (Socialize -> Talk about the group -> Relationships)
- Get gossip from the other members of that clique; I go for the leader (Socialize -> Talk about the group -> Gossip)
- Be annoyed about who's doing it.
Entire cliques will bully one person, hence there are multiple bullies. If you can get the leader of the clique to stop, the rest will too. You can also use influence to tell one of the members of the clique to let-up (which may in time eventually have them stop bullying, I think).
How you go about it is up to you. You can transfer influence (at a loss) from one idol to another by asking them to get blackmail on another, though that may fail and you'll be out the influence. You can move the leader of the clique to a different group (this is the most direct and quick method if you don't have influence over the leader), and I think you can also hold scandal points over their head too, though I've never tried.