You say that there is a bounty on someone's head and then there's a bounty on their head. There is no formal bounty posting system; it is completely player controlled. It usually helps if you post about it in the Trader's Lounge. Be sure to provide conditions (alive or dead, and that's about it) and be sure to pay out the bounty to whomever turns in the character.
I'm sure a bounty hunter can elaborate more if I happened to miss anything.
I'd recommend contacting a bounty hunting faction over a merc faction, but I suppose you could contact all of them. Commerce forum works for public bounties; sometimes others will add to the bounty if they know of the individual. Many factions (primarily governments) do also post some public bounties on their websites for bounty hunters to peruse. But generally bounties are in at least the tens of millions (often much more, depending on the target), if you wish for them to be actively pursued.
One day we will talk Togan into coding a bounty DB for everyone to use. >.>