I don't know if she is set on Bermuda for a particular reason but it wouldn't be my first choice for a first timers cruise.
Anyway, of the ships listed on that doc that Dave posted - we have been on Royal Caribean's Explorer of the Seas and NCL Norwegian Dawn. Both are gorgeous ships but they offer very different experiences. RCCL offers your traditional cruise experience with assigned seating for diners and a more casual option. NCL offers only freestyle dining which in our experience was just us sitting alone and never had much experience to enjoy the company of others at dinner. Personally, when I cruise alone with my husband - I enjoy being seated at dinner with others - gives you an opportunity to meet new people and get a break from 7 straight days of listening to your spouse (Melissa - you met Doug - you know what I mean lol).
Anyway, if they are not 100% for Bermuda my recommendation would be to cruise on Celebrity. That is my favorite. Not many kids (if I'm leaving mine home, I really don't want to see other people's), the food is superb, and the service wonderful. Since you said money's not really an issue, If they book a suite, they get a butler which is most excellent! If you have any more questions, you know where to find me
