We've been to Bermuda four times, two of which were in the past two years. We were on different ships, though.
Explorer of the Seas will dock at King's Wharf, aka Royal Naval Dockyards, located in Bermuda's West End. The area has a lot of history, and is now home to many shops (including Bermuda Rum Cake Factory) and a fabulous museum. The famous south shore beaches, which I highly recommend, are a bus ride away. You'll want to take the #7 bus, which stops pretty close to where the ship docks. If you prefer, you can take a ferry into the city of Hamilton, which has a lot of shops as well.
Happy to answer more questions....just ask away!