Limiting who can bump would be easier to implement, but the roughness/immediacy of it makes it more easy-to-manipulate IMO.
Why don't you make it so the thread can only be bumped to the top once per day max? That seems like fair compromise and would certainly defeat the purpose of the paid bumping whilst still allowing active threads to be bumped.
I have idea.
Whoever writes less than 300 characters can't bump thread. Quotes are excluded from this.
Meaning: more time to write post == less posts == less spam. If that doesn't work (and I think it should), increase minimum character limit to 400. Or 500. This rule should be applied to every rank including thread starter. Show them who is boss here

This wouldn't work either. The bumpers would then just start writing posts that contain 300 characters. They'd probably be more of an eyesore than the generic good project ones etc.