Looking at the last 6 months on SO:
count(*) [Total Bounties],
sum(case when UserId = -1 and TargetRepChange is null then 1 else 0 end) [Lapsed no Answers],
sum(case when UserId = -1 and TargetRepChange is not null then 1 else 0 end) [System Awarded]
where VoteTypeId = 9
and CreationDate > GETDATE() - 6*30
- 6495 bounties ended
- 1129 were awarded by the system
- 1920 lapsed without any bounty being awarded
In close to 50% of the cases the system decides what to do with the bounty.
So yes, auto acceptance is incredibly common in the bounty system.
note: data explorer is missing some data required to perform this analysis.