I really don't like any (extra) feature that will encourage people to think of Stack Exchange as a place where they can get rapid answers. Most of the questions I happen upon that appear to somehow be in urgent need of an answer are at the far end of the quality spectrum, because OP is on fire and doesn't really have the time to write a good question.
I feel that what you're proposing might encourage answerers to give even quicker answers, that may be extremely beneficial to the OP ("Hey, here's a link that solves your problem") but not so much to the community.
And when you come upon a question with an immediate bounty, are you going to spent any time trying to improve it? Or are you going to start answering immediately? Well you might actually go for improving it, as you've done with quite a few posts on Programmers, but I don't think most of us will.
In most cases, when a bounty is set, there are already answers, so in order to get it you have to provide a better one. We don't want to encourage a culture of quick answers, we strive for expert answers. And those can only be quick in very specific scenarios (trivial questions).