Quick question on the "early morning transport to Haneda" topic...

I am on AA's 6:40am departure on a Monday morning. It looks like there is a "limousine bus" service from the Shinjuku area that is scheduled to arrive at the HND international terminal at 5:15am. If I read the schedule correctly, the bus makes some pickups at the Hilton, Keio Plaza, etc. before reaching the pickup point at Shinjuku Station at 4:45am.

I am staying near Shinjuku station and would like to get the bus there at 4:45am. But I am a bit concerned that the bus might fill up - I have taken it from hotels before and the hotels make reservations (iirc). Does anyone have any experience on whether the (early morning) bus is sometimes full before it reaches the Shinjuku station pickup point? Or is there some way to make a reservation if not catching the bus from a hotel?

Thanks!