I got to thinking...
Should questions with an open bounty get bumped periodically? Maybe once halfway through the bounty.
.. is sufficient.
As with all questions, if you are finding that people are not answering, you have a few options.
At this point, you have already gone to step 3, so I'll consider steps 2 and 1.
Re-read and edit
Re-read your own question. If even twenty minutes has passed, I will find that even my most carefully considered questions seem very different once I publicize them. You might discover that there is contextual information missing, or irrelevant information contained. Try making it shorter or longer. The people on SO have a limited amount of time, and they will give up on questions for their own reasons. Small edits can have huge impacts.
Check the answers or comments (if any) they may indicate where the disjoint is between you and the community. If they ask for clarification, clarify, if they ask for more information, give it to them. This will show you are engaged, and it will be more likely that they answer.
And of course, each edit gives you a bump, regardless of having a bounty or not.
Do More Research
Most people will do a simply google/bing search before they post their issue onto SO, but it is entirely possible that the comments or answers, despite being wrong, can still give you clues that enable you to do some extra research. Maybe it will help you find your answer and maybe not, but it should enable you to add extra contextual information to the qusetion which means an edit. Every edit gives you a bump to the top of the active page, so once again you will generate extra interest.
As Jeff says, you are already getting some bonuses from adding a Bounty, however it doesn't mean you should just give up and assume that your job is finished. Adding a bounty to a bad or unanswerable question does not make it answerable. It also doesn't mean that the problem you originally had will go away.
Bottom line, if you remain engaged, your question will stay in the active page, and you'll get more responses. Oftentimes, if you do that, you won't need the bounty at all.
I've had a few bounties that after making the question a bounty I only saw probably 20 or 30 more views and no new answers or anything. You put a bounty on something to get it answered. Not as the creator of some competition
So bounties could be bumped maybe every day of the bounty. This way the question has a much greater chance of being seen. I mean, who looks at the bounty tab exclusively?