Quote from How does the bounty system work?How does the bounty system work?:
How do I start a bounty? When can I start a bounty?
A bounty can be started on a question two days after the question was asked.
To start a bounty, click on the start a bounty link at the bottom of an eligible question. The bounty panel will open. Use the dropdown to allocate the bounty amount -- anywhere between 50 and 500 reputation, in 50 point increments.
You must have at least 75 reputation to start a bounty, and at least as much reputation as the bounty amount.
The bounty award will be subtracted from your reputation when the bounty is started, not when it is awarded.