Not sure if you can rent bikes in advance or not, but I certainly wouldn't say that they "have very few bikes". I'm sure they're doing a balancing act of having the right number to satisfy as many guests as possible during the busy season, without having so many that it's unmanageable and too costly for the slower times at the resort.
The resort has always been very helpful in finding another place for guests and members to rent bikes. I know in the past, the outside places have always matched the resort's price, although I don't know for sure if this is still the case.
Sunday is the BIG check-in day at the resort, due to the high points required for a Saturday night stay. Many people stay nearby the night before and check in at the resort early Sunday morning so they will have access to the facilities. If you arrived late in the day on Sunday, this could explain why all the bikes were already rented.
Hope this helps!