I don't understand why the source of the wound matters. When you place a bounty, the intent is to get the character wounded. (And, yes, perhaps have it be bad enough that he loses his office.) Sure, you may feel like you wasted your gold, but one way or another you lost the gold the instant you set the bounty. If you're lucky, maybe some lucky warrior in your own realm got it. 
Think of when you are haggling with someone. If they need to get their money out of it, you are more willing to pay that higher price, but if they got it for free you aren't going to want to pay top dollar for it. Its not exactly the same but you get the general idea of it, I hope.
