Is there a way to search only unanswered questions with an open bounty on StackOverflow ?
As of the date of this post, there isn't a way to filter on whether or not a question has a bounty on it.
The closest you can get is
See the clickable Advanced Search Tips on the search page for more options.
I should add that maybe you don't want to be doing this. Just because a bountied question has an answer it doesn't mean that it is answered. I've received a bounty before when 3 answers were posted before mine.