We didn't stay at the Fairmont hotel so don't think that is a requirement. We simply called and made a reservation from where we were staying and took the bus over. There is a free shuttle from the gate up, so you don't have to make the long walk if you don't want to.
The cost for club rentals, cart and 18 holes for two was around $210, but very worth it for our biggest splurge of the trip. Neither of us is a golfer. We hack our way around any par 3 course and pick up half the time. This course is beautiful and challenging. Just playing on it forces you to improve your game. I think the back nine may be the best I have ever played. Lost three balls on the front nine and none on the back.
We played late in the day when the course was empty and never felt rushed at all.
We are already talking about another trip to Bermuda in the fall and this is the one thing we definitely will do again.