Help me get a clearer definition of your question. Using your example, are you saying that:
.... starting on May 3 you do not want any more reservations at all, ever, and how do you block your calendar? (block remainder of calendar)
.... that you want no reservation on the night of May 3 and would be willing to have new guests check in on May 4? (block only one night - one time only)
.... that you want no reservation on the night of May 3 and would be willing to have new guests check in on May 4 and you always want a calendar rule that 24 hours are needed before you accept a new guest after a guest checks out? (create a rule for your calendar)