So according to the FAQ:
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your own answer.)
If you do not award your bounty within 7 days (plus the grace period), the highest voted answer created after the bounty started with a minimum score of 2 will be awarded half the bounty amount (or the full amount, if the answer is also accepted). If two or more eligible answers have the same score (their scores are tied), the oldest answer is chosen. If there's no answer meeting those criteria, no bounty is awarded to anyone.
What if the top voted answer is totally incorrect - it doesn't seem right that an answer that is completely wrong should be awarded a bounty purely because it's the only one that's reached 2 votes, or it's the highest out of a whole series of wrong answers?
Is there no option that 'none of the answers was of good enough quality to earn the bounty'?