Sometimes a person answers a bounty question really quickly and the answer is even accepted.
Due to the following points listed on the set bounties page:
It is your responsibility to award the bounty during the seven-day period or the 24-hour grace period that follows it. You will receive several e-mail and site notifications as the bounty period draws to a close.
You must wait 24 hours before awarding a bounty.
The OP forgets to give the bounty even when he/she had mentioned it. This has happened to a number of people and myself many times.
There are two questions with similar queries:
My proposal for the same
Once the answer is accepted by the OP, the person who answered the question should get the priviledge to send out a notification to the OP after a day and only one notification per day should be allowed