The way I see it, there´s going to be two kinds of bounties.
The first kind are for things that are pretty much universally agreed to be war crimes - using NBC weapons, burning down a city for shit and giggles, talking in the theater, that sort of thing. Whoever issues the bounty is going to deposit the money with either ComStar or the MRBC, depending on the era, after ComStar/MRBC have reviewed the issue, so that everyone who considers going after the target knows that, firstly, their target is legitimate, and secondly, they´re really going to get the money.
The second kind is where someone - Sunnyboy Liao, some petty noble, or whoever - promises X amount of C-Bills for whoever brings him the head of a particular person or a member of a particular unit. To collect, you have to show up and present your catch, either in person or to a representative of whoever issues the bounty. Anyone who considers going after that target knows that, firstly, it´s anyone´s guess if the target actually did something wrong other than annoying someone with too much money, and secondly, it´s anyone´s guess if they´re actually getting paid, and if they´re going to survive turning in their catch instead of being turned into a very convenient dead hero for the local propaganda efforts.