Currently, the auto-accept rules state that in order to be eligible for auto-accept, the answer must be given after the bounty was started, and receive 2+ votes. I think that pre-bounty answers with substantial post-bounty edits should be eligible as well.
Only the votes received after the first post-bounty edit should be counted to decide what answer gets auto-assigned the bounty. For tie-breaking purposes (i.e. when the oldest answer among the post-bounty ones with the same vote count wins) the time of the first post-bounty edit should be considered.
The rationale behind this change is that it gives improving an answer an equal treatment with giving a new answer for the purposes of bounty hunting.