Yesterday I've offered a bounty for this question, but after a while I've found my own answer. Now I can't see any reason to keep offering that bounty. Is there any possibility to withdraw it?
You can't withdraw bounties. You already received a significant part of the benefit of a bounty as the question was bumped and received increased attention due to being featured for one day. Allowing users to exploit refunding bounties to get increased exposure for free would be problematic.
Technically, moderators have the ability to refund bounties. But that ability is meant for cases where questions need to be closed, but received a bounty. It is not used in other cases, and it would not be appropriate to use it in this one.
No. It is not possible to withdraw a bounty. See the help center, particularly:
You may not cancel a bounty once it has been started.