One of my questions had not so good answers and I would start a bounty right now.
Why do I have to wait so long?
From the FAQ
Questions must be at least 2 days old to be eligible for a bounty.
so I think that it is actually two days that you have to wait. I believe that the reason is to give people a chance to respond before putting a bounty on it. If you believe that your question is too far down the main page try editing it if you have more information and that will bump it up.