Some basic guidelines on how bounties work From https://superuser.com/help/privileges/set-bounties and https://superuser.com/help/bounty.

After the bounty ends, there is a grace period of 24 hours to manually award the bounty. 

 - Simply click the appropriate bounty award icon next to each answer to permanently award your bounty to the answerer. 
 - You cannot award a bounty to your own answer.
 - You can accept an answer without awarding a bounty to it.
 - You can award a bounty on an answer without accepting it.
 - Awarding a bounty cannot be undone.
 - If the bounty was started by the question owner, and the question owner accepts an answer posted during the bounty period, and the bounty expires without an explicit award then we assume the bounty owner liked the answer they accepted and award it the full bounty amount at the time of bounty expiration.
 - If you do not accept an answer nor award the bounty within 24 hours of the bounty period ending, half the bounty value will be automatically awarded to the top voted answer posted after the bounty start, provided it has a score of at least 2.
 - If two or more eligible answers have the same score (their scores are tied), the oldest answer is chosen.
 - If there's no answer meeting those criteria, no bounty is awarded to anyone.

The guidelines don't mention splitting the award between multiple answers.  I thought I saw that somewhere, but apparently, I was mistaken.  Given that the award can't be changed, it looks like it all needs to go to a single answer.

The guidelines also don't describe what happens if you accept your own answer and don't explicitly award the bounty to another answer.  It looks like the bounty would simply be lost in that case, since the system would award it to the accepted answer, which would not be eligible to receive it.

Bottom Lines:

 - You've written your own answer.  If you plan to accept it (which would be logical, since it describes your actual solution), either wait to accept it until after the bounty is awarded, or manually assign the bounty to avoid it being lost and wasted.
 - You could also accept another answer if you think it's worthy and want the author to receive the acceptance rep.  That answer would also receive the bounty if you don't award it elsewhere.
 - If no other answer attracts at least 2 upvotes, manually award the bounty or it will be lost and wasted.
 - If another answer attracts at least two upvotes and you would be happy to let the system award the bounty to that answer, award it yourself so that half the bounty isn't lost and wasted.