I have cruised to Bermuda twice. Once from Boston on Celebrity Meridian. That ship docked out at the Royal Naval Dockyard. The bus service or ferry made it easy to get to Hamilton. I really love Bermuda. It is peaceful and pleasant there.
I also sailed there from NY on Home Lines, Homeric. Wonderful ship and fantastic cruise line. Sadly they have gone away. I would choose them over any other line if they were still operating. We docked in Hamilton on Front St. I have to admit it was a lot handier there. Easy walk to the bus station to get busses all over the island. The shops or downtown were always busy and lots of fun to explore.
I have often wondered why the major lines have not been sending ships from Florida there. A ship leaving from Miami or Ft Lauderdale could make a stop at Nassau then on to Bermuda.
Both of those trips were in the 80's so I am not up on the changes in Bermuda. Some people rented scooters and went off on their own to investigate the beaches. Lots of nice places to stop and swim there. I do not remember either ship selling shore tours there. We always made our own way around. One of the things I loved about Bermuda was there are no vendors constantly harrassing you to buy junk. This island is a lovely peaceful paradise that should not be missed.