I would shy away from the idea of villages offering bounties on just anyone - as already pointed out, they could just use their own ninja for it. On the other hand, I could see them offering bounties for really tough targets. If you were the Village Hidden in the Mist, for example, would you want to risk, and possibly loose, some of your best jonin trying to take out someone like Kakashi? Or would you rather just pay some other poor smucks to take the losses?

One way I could see the whole system working is for it to be run by an underground organization who combines multiple bids - so its not person x saying "I'll pay 5 mil for you to kill Asuma"; its person A contacting this organization and saying "I'll toss 50,000 in if you get rid of Asuma", then person B contacts them and says "Asuma interfered with my operation, add 20,000 from me to the bounty", then person c adds say 75,000, and so on and so forth until you end up with the 5 mil.

If someone actually HAS 5 mil and considers it worth spending it all to take out Asuma, they go to a village and hire an assasination mission, which is probably going to be more reliable and faster. But if they don't have that much or aren't willing to spend it, they contact the bounty organization and put down what they can afford in an effort to encourage folks to take him down without having to pay for a full assasination.