Who are you dealing with at Fairmont? Where are you having your ceremony & reception? I've been to the Southampton, so I might be able to help you a little bit. Also, do you know that they have a HUGE spa & salon in the hotel? You could book hair & makeup right there. I dont know what time your ceremony is, or what day, but you've got to make sure you watch your timeline in Bermuda. If you were planning on going to a salon, business hours can be a little different and the only way to get around is public transportation or taxi. so, you'd have to make sure to allow for wiggle room.
Let me know if I can help you with anything. Good luck!!