"Start a bounty" is shown under all questions, even answered ones. The reason for this is that for certain topics at least, the answers may change over time. Only allowing bounties on un-answered questions would remove the ability to bring focus to a question in the instance where the answer expired or became no longer relevant.
Starting a bounty will make the question that has a bounty on it appear under the "featured" tab, which can have the effect of driving more traffic to the question (since the question becomes one of a small number instead of one out of all questions asked with that tag or one question out of all of the questions on the site), which can have the side effect of increased voting and increased views on the question while promoting additional answers.
Bounties can be used for many reasons, including;
- driving traffic to a question (as above)
- be given to exceptional answers that you found particularly helpful as an additional reward
- get new answers or updated answers
There is no rule preventing you from putting a bounty on a question that already has an answer.