Unless this sort of question is discouraged, I'm not sure that a two-day wait before bounties can be set is really that sensible. Why not let users burn their rep if they so desire?
One reason against this is that questions with an open bounty cannot be closed. Relieving this would offer the possibility of basically buying a closing protection for one week despite the possibility that a question might be a duplicate, off-topic, subjective etc.
Another reason is that a question should be well-posed enough to get answers without a bounty. Adding a bounty should not be used by default, since it should be judged by the community (and possibly refined) first.
The reason bounties has a waiting period is because they are only supposed to be used after you put the effort into getting the question answered yourself. If you don't get an immediate answer, you are expected to improve, clarify, and document your continued efforts. These activities bump your question to give it more exposure. Bounties are an escalation of that process.
If, after 2 days, you still don't have an answer you like, you can offer a bounty. Slice off a bit of your own hard-earned reputation...
When bounties were introduced, there was a concern that an expectation would develop where you could only get good answers to your questions if you "paid" someone to answer it. Not so.
But when all other efforts fail, bounties come to the rescue... later.