I wasn't sure it was possible, but last night I tested it out. You can place a bounty and then immediately accept an answer for that question.
Purpose of Bounties
The primary function of the bounty system is to:
- Feature a question so it doesn't have to be bumped repeatedly
- Give people an additional incentive to add new and perhaps more comprehensive answers
I would also argue that a secondary function exists: provide other users an opportunity to gain a significant amount of reputation for a thorough and comprehensive or deeply researched answer (as generally the questions are hard to answer, or require special expertise or knowledge). This is a particular help to those that don't have much time to spend daily on answering smaller questions.
As implemented, though, it can be used without the top two benefits, and disallowing others the opportunity to provide a better answer by starting a bounty and immediately accepting it.
Further, as an accepted answer with a bounty cannot be changed, it should require additional consideration.
Worse, it is possible that it may be considered gaming the system, or provide people a way to engage in other undesirable behavior.
- Disallow acceptance of a bounty until 24 hours after it was started.
While some might use this functionality to provide an 'extra' reward to a particularly good answer, that answer will still be there in a day, so it won't prevent this functionality. It should only affect those that seek to short circuit the purpose of the bounty.