This would probably be a difficult feat, but could we have a badge for winning your own bounty? Maybe something along the lines of "Self-Poacher".
Would anyone even qualify for the badge right now?
Since you can't accept your own answer to a bounty question, I assume you mean "your own answer is the highest-voted answer at the end of the week."
Would you get half your bounty points back, in that case?
Badge is an interesting idea, though.
You should be a be to recall a bounty you put out, if you figured out your problem, but I don't think doing that should be rewarded with a badge.
To kind of steal from one of Joel's comments in an early podcast, I don't think Napoleon would have given you a little piece of colored cloth for doing this.
If there were methods to define your own private badges, you could do that and still be hidden from the others - if that makes you happy. In general, the ability to have your own near-real-time metrics about your performance might be an interesting thing too.