I don't think the current functionality or Ben Brocka's solution is the right way to go. There's something unsatisfying and unresolved about allowing the system to award the bounty based on an algorithm: the whole point of the bounty—at least to me—is to reward a person, not a post, for coming to the rescue.
So I'm partial to Servy's solution, where you can choose a contributor instead of an answer. This, as mentioned in Servy's answer, is not without its faults, biggest of which is the fact that it would introduce a new UI just for awarding a bounty.
Instead, I like yoda's suggestion the most: allow the awarding of bounties to revisions, not just posts. I think doing so would capture the spirit of awarding a contributor while being able to work within the UI as it is today.
Here's how I could see it working:
You can continue to award bounties as you do today. If you do so, it gets awarded to the post owner as normal.
Additionally, if you view the revisions list on an answer, you can award a bounty to any revision available. The bounty would then be awarded to the person who made that revision, not the post owner.
This would preserve the current simplicity for most users (the so-called "80%") while allowing people to handle the edge cases—like community wiki—for power users.
Of course, there's still a problem of discoverability for both bounty awarders and people looking to collect a bounty. But, if you're not sure how bounties work now, the current UI doesn't help that much anyway:
This question has an open bounty worth +50 reputation from Retrosaur ending in 3 days.
The current answer(s) are out-of-date and require revision given recent changes.
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I wonder if the whole issue of discovering how bounties work could be solved by a "how do bounties work?" link or tooltip with a short blurb that explains:
Bounties are awarded to the post or revision the person placing the bounty feels best answers the question.
Or something to that effect.