Hi, Well...Bermuda is not exactly in the Caribbean but it's in the Atlantic. We don't have a gay/lesbian resort on the island...but there are a number of quiet, romantic places to stay. Much depends on what you are looking for and how much you want to pay. I can only really think of one place on the island where you would not feel comfortable - it's a "Christian owned guest house/hotel" which routinely hosts all sorts of relgious groups for retreats and seminars.
Last summer Barb and I stayed at Pompano ...and had a wonderful weekend. I think all of the rooms overlook the ocean... it has a small beach, tennis, golf, dinner, entertainment... I would highly recommend it... I've also stayed in and worked at a number of other places on the island...so if you want any additional information on this or any of the other places on the island, send me an email.