On an old question with no accepted answer, the user sees a "start a bounty" link/button:
After clicking this they get the following:
My suggestion would be to move the "What is a bounty?" link outside of the "start a bounty" box. I can see a user being afraid to click "start a bounty" because they don't know what a bounty is, and they don't realize that clicking the button brings up another menu (as opposed to starting the bounty immediately).
You may also want to change "What is a bounty?" to simply "What's this?". That seems to be how most other "cool" sites are wording it nowadays. And everyone wants to be like the cool kids.
Edit: Here's a mockup of what I was thinking:
Another suggestion was made by dbr below.