My opinion would be, by approaching with the idea for a question to be eligible for Bounty , it should be two days old .
So before Accepting answer which is Self-answered , i guess Giving that Two days Bounty eligibility days as time period for Interested Answerer , would be Better and Logical choice. It provides a fair share of getting a better or equivalent answer and also a cleared view of what should it contain from other answers whilst Self posting it .However, sometimes they can be much better than you can add , so availability of chance matters.
Otherwise , you can put P.S. or NOTE or a comment stating that Answer from the Asker is also intended or Expected as in a Tutorial Format .So the interested Answerer could or would suggest the content in the answer(which ofcourse would be brief , and it also helps in gaining reputations from community, like a fair chance) ,according to him. Thereby making it a better QA.
As Jeff Atwood said here
To be crystal clear, it is not merely OK to ask and answer your own
question, it is explicitly encouraged.
I do it all the time! For example, when I ran into a nasty issue with
Java exploits in Google Chrome when browsing for images, I documented
that on Super User by asking and answering my own question. Now,
others can benefit from my misfortune — and best of all, I got new
even better answers beyond what I offered! Overall, a huge win all
So availing a time period for interested answer would be good enough , or If you are Confident enough to post it as Answer and accept it quite soon, both are welcomed.