A bounty will only be awarded under three specific circumstances:
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.
If the bounty was started by the question owner, and the question owner accepts an answer posted during the bounty period, and the bounty expires without an explicit award then we assume the bounty owner liked the answer they accepted and award it the full bounty amount at the time of bounty expiration.
Considering that the answer that was awarded the bounty is neither accepted nor was posted after the bounty was started that means that options 2 and 3 are ruled out and so you must have manually awarded the bounty. That means one of two things happened: you either clicked the wrong answer to award it to or a bug occurred and the system mistakenly awarded it to the wrong answer.
Just to be a bit more concrete to "prove" that the bounty was manually awarded you can see on the answer's timeline that it is attributed to you: "bounty end Vogon Poet Winning bounty for question Id = 218842". Whereas if it is automatically awarded Community takes ownership of the bounty as we see here on a random SO bounty by myself as it was easy to find: " bounty end Community♦ Winning bounty for question Id = 42162258".
Unfortunately unless you can prove you did click the accepted answer and didn't misclick and so it was a bug not much can really happen in terms of reversing the bounty to give it to the other answer.