Just back from a week in Bermuda. It is not a destination you need to rush to for the beer, despite its British heritage. Frankly, the bar/restaurant scene reminded be a bit of Niagara-on-the-Lake ten years ago, if I had to sum it up. Nevertheless, if you find yourself there for other reasons, you might be interested in the following.
There are two local breweries, Dockyard and OnDeRock. Both have very light distribution on the island, and brew draught only.
Dockyard brews five beers. They are available only at the Frog & Onion, out at the far tip of Bermuda in the Naval Dockyards area (also the main cruise ship port in summer, but there is very light traffic at this time of year), and at a couple of pubs in Hamilton under the same ownership group: the Hog Penny and the Pickled Onion. Cass said above that the beers are brewed to appeal to the tastes of a typical cruise ship passenger, and that is a good summary. The Lager was sweet, the Porter was decent but with a rather off-putting metallic nose, the Amber reminded me of Ontario craft circa 1995.
I had better luck with OnDeRock. They say they make six beers, but I only encountered three, and believe me, I searched. The good news is that the IPA was really quite decent. About like a Great Lakes Canuck, say. A definite winner in a sea of mediocrity. OnDeRock IPA is available at the Henry VIII pub (closest thing to a true pub that I could find, at least anywhere near me at the Southampton Princess), the Boundary Bar at the Turtle Hill Golf Club (on the property of Southampton Princess), and Flanagan's in Hamilton. It is probably also on at The Robin Hood, Henry VIII's sister pub in Hamilton, but I didn't make it there. That is about it, AFAIK. OnDeRock Pale Ale (also decent, not quite as good as the IPA) is available in the bar at the Port Royal Golf Club.
As an aside, that craft beer bar in the basement of the Southampton Princess that Cass mentioned has been turned into a coffee shop.
I stayed at the "South P", as the locals refer to it, so I didn't see as much of the eastern half of the island as I might have. But research did not turn up any other likely candidates for good beer. I did a day trip to St. George and stopped in at the White Horse, the main pub in town (right on the town square). The barman said they did not carry OnDeRock and he did not expect it to be available anywhere out that way.
At any bar in Bermuda you are virtually certain to encounter some combination of the following on tap: Stella, Heineken, Carlsberg, Sam Adams, Boddington's (nitro) and Guinness. That is it. Apparently Carlsberg Elephant Beer in bottles in also popular amongst some locals. I had a couple - it is not terrible.
So the best bet is to be somewhere within striking distance of one of the few pubs above. Otherwise, develop a taste for Goslings Black Seal Rum and the ubiquitous Dark & Stormy!