Bounty logic is relatively sensible, but not particularly well documented. There is a comprehensive post on meta.se about how it works, though.
In short, in your case, if you offer a bounty, you will never get any of that rep back, even if you accept, or answer your own question.
If you award the bounty to anyone other than yourself, the entire bounty goes to them.
Otherwise, when the bounty-period ends, if the bounty was offered by the question asker, and they accepted an answer (that was not their own answer), then that answer is given the entire bounty.
Otherwise, the highest-scored answer given after the bounty has been offered will, if the score is 2 or more, be awarded half the bounty.
If two answers given after the bounty was offered, both share the top score, then the oldest one will be awarded the half-bounty.