This hasn't happened to me yet, but there should be a reward when someone adds a bounty to my question. I was thinking either a rep increase or a badge. The reason is because someone found my question worthy enough to pay with his/her own rep to find an answer to it. I would want a badge for that!
What do you get? Hopefully, a good answer to your question, and one that you didn't have to pay for yourself with your own hard-earned reputation.
You probably also get an upvote, and maybe someone's earnest attempt to clean up and improve your question to attract the best answers possible, around the time that they set the bounty.
And then the attention attracted by the bounty causes prospective answerers to look at your question, and several of them probably upvote it as well (at least, if it's worth upvoting!).
Each upvote on a question nets you +5 reputation. Good answers to a problem you have are invaluable.
Badges are mainly used to encourage behaviour that we want to see more of. There are already a lot of badges that you can get from asking good questions, so I see this as redundant.