Yes, this is a good idea, but which contains some problems :
- It's not player-driven at all. You pay, NPC work for you. This is bad, but at least, it's better than no bounty hunting system at all.
- Players could abuse this easily, because we know big factions got hundreds of thousands of caps. In my opinion, it can be fixed by setting a maximum price you can pay for someone's head*.
* You pay for two things : The Bounty Hunters' strenght AND the amount of encounters the hunted dude will meet. For example, 5000 caps for raiders-like bounty hunters and 5 encounters. All these parameters, at the maximum, should not go above 10k caps (for example), and you can't set more than one bounty over someone's head. This way, a character, even hated by everyone, can only have one bounty of maximum 10k worth over his head.