When viewing your own question which isn't 48 hours old yet, you'll see a link "question eligible for bounty in x hours/days":
When you accept an answer, the link isn't shown. Is there any particular reason for this? Perhaps you want to give an extra reward to a quick answer; it'd be nice to know when you can actually do so. The 'start a bounty' link is always shown, even if you accepted an answer.