Scott,
I currently live in Bermuda and dive with Blue Water Divers as well as Dive Bermuda. Both are high quality operations and you can't go wrong with either.
Blue Water Divers operates in the three locations: Wyndam Hotel, Somerset Bridge Marina, and Elbow Beach Hotel. The Elbow location is just for shore diving, they have no boat there. The Wyndam location is a full service hotel, and they keep a boat there in summer months, although when there is less business, like now, you have to go to there Somerset location. The Somerset location is not a hotel, just simply a marina, so only accessible via taxi, but that is where most of their charters leave from.
Dive Bermuda operates out of the Hamiltion Princess and Southamption Princess, with boats at both locations. The Southamption Princess is more of a resort, with beach, tennis, pool, etc. The Hamilton Princess is located in town overlooking the harbor, and has more of a business feel to it.
Timing of your trip is important. After September, the tourist season winds down and sometimes charters won't go out during the week due to lack of interest. Certainly have your friend call down and see what there plans are during the time you are comming down. Check water temps as well at
www.weather.bm . Click on the marine tab and scroll down to get the latest on marine conditions. Right now, a full 3ml is best.
The other major operation is Triangle Diving, which operates out of Grotto Bay Hotel on the opposite side of the island. No direct experience with them, but I've heard all good things about them from other.