I offer a bounty for this question
But I have not always the time to test the solutions at once. To trigger my error I have always to make a cold boot. So my question is, can I give the bounty after the bounty period?
No, you can't. You'll have to award the bounty now (or in the next 24 hours, the so-called 'grace period'). If you don't, none of the existing answers will get the bounty and if you do want to award one of them which turns out to help you, you'll need to post another bounty (and remember that each time the amount needs to double). Or just upvote and accept it, that already gives 25 reputation.
Your situation (not being able to test answers while having an active bounty) is quite rare and hence the system doesn't accommodate it. You'd need to plan such things in advance, just like you shouldn't post a bounty a few days before your vacation. Some Stack Exchange site have a list of bounties with no deadline (example) but I'm not aware of such a topic here, and neither do I know how effective such topics are.