When I post a question with a bounty, the question generally captures more votes, and I get more rep than I would have otherwise.
In cases where I've offered less than 150 (100 from me, 50 from SO) bounty, I've generally received that reputation back in upvotes.
In other words, by and large, it's free to post bounties with less than 100 of my own rep in the bounty.
Does the SO data dump contain enough information to figure out the site-wide average where a bounty is 'free'?
It would require data on when various votes were given (ie, votes before adding the bounty wouldn't count), the amount of the bounty, etc.