I disagree : the bounty is for an action to be performed by ANY player upon the target : the bounty-setter rewards the action being done, that's all they have paid for. Who eventually does it, and for why, is not for them to restrict or limit, nor should the game do that for them.
Its for the bounty-setter to decide how much to offer ; enough to get it done, not so much that profit (or a reduced cost) can fall to their target who may choose to 'short-circuit' the process and do it themself. Remember, the target has to bear the cost of any such self-cleaning, in cards and risk : that should be enough or we are just on that road to the 'I attack, risk nothing and win everything!' folly once more...