The ticket office is right next to where the busses depart (roughly around bus stop #21 on the west side of Shinjuku station). This seems like a very small risk. How about stopping by the day before and buying your ticket in advance? Never done this so I don't know if they sell tickets for specific rides. But if they do, and IF -- this is a fairly big IF -- there is someone there who understands enough English to get the idea, that would solve the problem.

I think the reason for the hotel "reservation" is simply that without it, the bus skips the hotel.