A question appears on the "featured list" for 7 days from when the bounty is added to the question, regardless of when the bounty is actually awarded.
The bounty can be manually awarded at any time in those 7 days (although you must wait at least 24 hours from when the bounty was added, and the bounty can only be added at least 48 hours after the question ...
From: How does the bounty system work?
What happens if there's no answer after the bounty period?
If after the end of the bounty period a question has no answers, no
bounty will be awarded and the question will no longer be featured.
Bounties are best understood as exchanging reputation for higher
question visibility and increased answerer ...
As stated on What is a bounty? help center, generally the bounty is non-refundable.
It is funded by the personal reputation of the user who offers it, and is non-refundable.
All bounties are paid for up front and non-refundable under any circumstances.
"Under any circumstances" also includes if the bounty giver doesn't get any satisfying answers....
To close out this discussion question as completed, I'm copying my comments here as an answer:
According to what is a bounty: To avoid overly promotional bounties, if you are offering a bounty on a question that you have already posted an answer to, your minimum spend is 100 reputation (not 50). Therefore you may have to double the bounty of 50 points to ...