I think as a first step we should have a new silver and gold badges. There are currently a handful of bronze badges which encourage dipping one's toes in the bounty system, but nothing beyond that. I suggest:

Mercenary: answered at least 20 questions with pending bounties, received at least 5 bounties

Bounty Hunter: answered at least 100 questions with pending bounties and received at least 20.

Or similar. Actual values to be tweaked as appropriate. They could also hinge on amount of rep rewarded, not the count, or in addition to the count.

I think as a first step we should have a new silver and gold badges. There are currently a handful of bronze badges which encourage dipping one's toes in the bounty system, but nothing beyond that. I suggest:

Mercenary [silver]: answered at least 20 questions with pending bounties, received at least 5 bounties

Bounty Hunter [gold]: answered at least 100 questions with pending bounties and received at least 20.

Or similar. Actual values to be tweaked as appropriate. They could also hinge on amount of rep rewarded, not the count, or in addition to the count.