If I decide that an answer received on a question I ask is particularly useful, is it acceptable to start a bounty and award it straight away?
There's a 24 hour wait period on awarding bounties after they have been offered. If you try to award it sooner, an error message will display notifying you that you can only award it after n hours, where n is 24 hours minus the number of hours that have elapsed since the bounty was offered.
There's no official name for this that I'd be aware of, so I'm calling it "the bounty escrow" myself, but it is described in the Help Center > Privileges > set bounties:
How do I award the bounty?
You can award a bounty by clicking on the respective button below the upvote/downvote interface. Note that:
- Community wiki questions are eligible for bounties.
- You can accept an answer without awarding a bounty to it.
- You can award a bounty on an answer without accepting it.
- You must wait 24 hours before awarding a bounty.
- Awarding a bounty cannot be undone.
See the link above the quote for more info, and some additional information (though not the 24 hour wait between offering and awarding bounties) can also be found in Help Center > Reputation & Moderation > What is a bounty? How can I start one?