That's an interesting corner case. Questions with bounties can't be closed and a bounty must run for at least 24 hours before being awarded.
For this year I propose: still-active bounties must be awarded as soon after the end of PTIJ season as the interface allows (you won't get your full week), and if that means moderators have to delay closing that question only by a day, so be it. We didn't anticipate the problem and it's a little late to spring a rules change now.
For the future I propose requiring that bounties be awarded before the end of PTIJ season, which means starting them in time to do that. Unfortunately the only enforcement here is that moderators can refund bounties, but that's not quite fair -- a bounty buys publicity, and refunding doesn't undo that. So we'll need people to be careful to actually award their bounties.