I'm not sure whether it's necessary, but you can always un-accept answers by clicking the checkmark again. If you leave a comment explaining it to the user, he won't need to wonder what's that about.

You need to wait 2 days or so for the bounty option to become available. There should be a tiny message below your question stating when this option will be available. If there isn't, try un-accepting the answer and reloading.

As the bounty is offered quite publicly, you should add a comment to your question stating that it's not about attracting additional answers, but to reward the user that posted the answer already.

You need to wait 2 days or so for the bounty option to become available. There should be a tiny message below your question stating when this option will be available.

Here's where the message appears for one of my questions:

At the same location, the message telling you when your question is old enough should also be visible.

As the bounty is offered quite publicly, you should add a comment to your question stating that it's not about attracting additional answers, but to reward the user that posted the answer already.