I thought this was already a thing but guess not..the suggestion would be to remove bounty from you once you kill the person who placed it.
Why? Well first of, because otherwise I'd have a good reason to kill the bounty placer over and over again without him doing anything to me. Why? Because he's responsible for every player hunting me down. Right now, even after I kill the placer, I don't really get anything from it since I'm still in the same trouble and everyone is still chasing me - meaning i still have a damn good reason to kill the bounty placer again.
If you want an RPish reason, who's gonna pay the hitmen if the person who placed the bounty is already dead? Of course this would mean the bounty should be canceled on his death even if it isn't related to me, which may still be a decent suggestion, i'll leave you to decide..
If however you find the first one better (me being the killer) please make it so if he dies near you, bounty gets removed..because someone might take the last shot and steal the kill (meaning you'd have to go and kill him again even though you assisted in killing him in the first place, which would be DM, i guess), or maybe the game won't recognize you killing him (like shooting a car on fire and killing the driver trying to get out doesn't get recognized).