Concerns have been raised in other questions that accept rate discourages asking hard questions.
In the light of that, wouldn't it be reasonable that expired bounties do not count towards the accept rate? If a bounty has been put on a question, and it has expired without an answer being accepted (or even auto-accepted), that's arguably proof that the OP did everything in his power to get an acceptable answer.
I'm assuming that the idea of accept rate is to identify those who just keep asking questions, without contributing to the community by marking answers as accepted, but correct me if I'm wrong here...? Based on that assumption, I don't see why the accept rate should be affected in said scenario, as that is obviously not what's going on.
If there were good answers, that the OP just did not bother to accept, they would be auto-accepted by pure virtue of being good answers, since it is a fundamental concept of the site that the quality of an answer should be reflected in its votes, so this scenario, too, should be out of scope for the discussion.