If someone needs a question right away, I would assume putting a bounty on it will expedite the answer process.
The reason for the delay is that bounties are only supposed to be used after you put the effort into getting the question answered through the normal means. First and foremost, you get great answers by asking great questions. If your not getting great answers, you are encouraged to improve and clarify your question and documenting your continued efforts. That's supposed to come first.
You don't want to create a system where there is an expectation that you have to "pay" someone to get the quickest and best possible answer. Bounties are a means of last resort to add awareness to your question through added exposure.
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...
After all other efforts have failed, bounties may be used to add a bit of emphasis to your question above all others; not by buying your way to the head of the line from day one, but later.