I went through the description of bounty and its terms / rules. However, I couldn't find what will happen if I have a bounty on my own question and I decide to close or delete the question.
Any experience with that?
If you already have a bounty running on a question, you would not be given an option to either close or delete the question.
If you want to close or delete question, for whatever reason, you can possibly flag the question and ask the moderator to refund the bounty, so that you can proceed to close or delete the question. Though I can't guarantee that the moderator will indeed refund the bounty as you wish.