Someone has opened a bounty onto one of my own questions.
What will happen if I accept an answer on this question? Whose reputation will be decreased?
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When a bounty is placed, the reputation is immediately taken from the person who placed the bounty. So, whatever you do - your reputation is safe =)
This meta question was the cause of the flexibility added to the bounty system and you can read about it in more detail on the stackoverflow blog. There's a paragraph that seems particularly relevant to your question (my emphasis):
Once awarded, you’ll see the bounty amount icon permanently affixed to the answer it was awarded to — and, again, all bounties are completely independent of and unrelated to accepting an answer.