No, not a bully.
But I would say that Frink has been pushing people’s buttons. It might be nice if he backed off of that a bit.
Oh but that’s just silly old Frink!
It’s not silly old Frink when it causes one to feel bad about it, as it happened with Warbler. The Wikipedia article on bullying says that there’s an imbalance of power a lot of the time with bullying. I think here people do think Frink is a level above them in clout. He’s a person that lot of people like or look up to. Warbler’s said he’s been bullied a lot in the past, that’s probably why he had such a bad reaction.