The way I see it is this way:
I can place a bounty on someone for the cost of a medal. I suggest this medal would be private (not emails telling them I sent it).
Other players can see that someone has put a bounty on my foe and can collect it if they eliminate them from a match. In turn for delivering the death blow, the eliminator will get the "Bounty Hunter" medal. The eliminated player will then have their bounty cleared.
I find the stackability of bounties interesting, say if someone has 3 bounties out on them, I can eliminate them and collect 3 medals.