Should the following functionality be altered?
If you post a question and then delete it yourself, you can wait 2 days and undelete it and then immediately post a bounty. IMO it should require 2 days of the question existing (visible) on the site for it to be properly allowed to support a bounty.
If this isn't required then IMO then a bounty shouldn't have a time required to be posted.
In addition I have asked the same question twice that received downvotes without a bounty, but it doesn't with a bounty.
If someone wants a good, fast answer as quickly as possible then posting a bounty immediately makes sense to me. So it is directly to the poster's benefit.