Think of it as putting the points in an escrow account :) Once you've committed the points will probably get awarded to someone, so they're immediately removed, and then when you get an answer they will be transferred to whoever you choose.
from the faq (excuse the terrible formatting, it doesn't copy nicely):
There are a few other rules around bounties:
Questions must be at least 2 days old to be eligible for a bounty.
There can only be 1 active bounty per question at any given time.
Users must have at least 75 reputation to offer a bounty, and may only
have a maximum of 3 active bounties at any given time. The bounty
period lasts 7 days. Bounties must have a minimum duration of at least
1 day. After the bounty ends, there is a grace period of 24 hours to
manually award the bounty. If you do not award your bounty within 7
days (plus the grace period), the highest voted answer created after
the bounty started with at least 2 upvotes will be awarded half the
bounty amount. If there's no answer meeting that criteria, the bounty
is not awarded to anyone. If the bounty was started by the question
owner, and the question owner accepts an answer during the bounty
period, and the bounty expires without an explicit award – we assume
the bounty owner liked the answer they accepted and award it the full
bounty amount at the time of bounty expiration. In any case, you will
always give up the amount of reputation specified in the bounty, so if
you start a bounty, be sure to follow up and award your bounty to the
As an additional bonus, bounty awards are immune to the daily
reputation cap and community wiki mode.