Tuesday may be a good day to go to St. George's, Bermuda's first settlement. It's a quaint town that gives a great sense of historic Bermuda. You can get there by ferry -- the ferry terminal is near the cruise ship dock. (The ferry ride is nice, in itself, btw.) On the way back, if you take the bus for your return trip, consider the Bermuda Aquarium Museum & Zoo. We enjoy zoos, and we were pleasantly surprised by this one.
Aside from the beach (yes, Horseshoe Bay is quite nice), what are some of your other interests?