Why do I see the 'start a bounty' button on questions which have an accepted answer?
See the screenshot below from this question
This is by design.
Bounties are no longer tied to accepted answers. Just because the OP liked an answer and accepted it, doesn't mean that the answer is sufficient for you.
You might still want an answer that goes into more detail or a cleaner way to solve the problem. So you still have the option to offer a bounty.