I covered this topic extensively here
I'll summarize it here.
[Mentioned in] Podcasts #26 and #34, [...] They didn't want a bounty to interfere with the 'normal' [usage]. If you're allowed to offer it right away, then it [might] create an economy where people only focus on questions with bounties.
Without bounties in the first 48 hours, we have a StackOverflow economy that is based on providing timely, quality, relevant answers to questions.
Downsides to immediate bounties
Cash Economy
[It could lead to users who] only answer the questions if the reward is rich enough.
Class System
The goal of StackOverflow is to judge technical questions based on their technical merits, [therefore] all questions should be treated equally.
There is no urgent tag
StackOverflow is not for people to come with time-sensitive questions. Most questions get answered very quickly, but it is not a guarantee and it shouldn't be relied on as such.
The Purpose Of Bounty
Bounties were created as a method to attract attention to questions which were missed on the initial run-through.
In the words of the FAQ
What if I don't get a good answer?
[...]
If, despite your best efforts, you feel questions aren't getting good answers, you can help by offering a bounty.
[Even] the FAQ says that "despite your best efforts". hat means if you've waited a few hours with no response, you can't just buy your way out of it. You should still be making an honest attempt to help the site by improving your question.
Final thoughts
Bounties do not improve questions
Bounties do not encourage equality
Bounties do not encourage quality
Please read the original answer for full explanation of these points.
