Negative effects of Bullying CS?

What are they?

Is it just the temporary negative modifier to relations, or something more permanent - influence drop per turn, other city states getting stand-offish, eventual perminent war, etc?

Believe it also cancels any quests that the CS was giving you. Id be interested in knowing if it also cancels future quests from showing up.

It won't cancel future quests. Once the relationships get back to normal, the CS will (randomly) start handing out quests again for you to enjoy.