Hi ell, and welcome to cruise-chat.
We've cruised to Bermuda four times, three of those were on Norwegian Majesty, most recently in 2005 and 2006.
Your idea to do the 5-hour island tour on the first day is excellent. We've done this tour through NCL and found it enjoyable and informative, and we'd been to Bermuda previously. Then, as you say, you can do the rest of your touring on your own.
It is very easy to get around Bermuda. I highly suggest the bus/ferry pass, and consider it the best use of our money. We purchased the three-day pass, but one- and two-day passes are also available. This allows unlimited travel in all zones on both the bus and ferry on consecutive days. We picked up our pass near the visitors center in St. George (cash only), but there are outlets near the major bus/ferry stations in Hamilton and the Dockyard, as well.
Here are some links for the transportation systems:
Each has its own links to the different routes and the schedules.
Going between the Dockyard and St. George is quickest and easiest by ferry (Orange Route). First ferry TO the Dockyard on weekdays was 11:15 am when we were there, but get there early as it does fill up fast. Again, check the current schedule.
Ferries between Hamilton and the Dockyard are more frequent, and you can take either the Orange or Blue Route. The ferry terminals in all three ports (Hamilton, Dockyard, St. George) is located very close to the cruise ship terminals.
The bus routes are very easy, and the buses are now air conditioned. The routes we used were the #10 or #11 (between Hamilton and St. George) and #7 (to South Shore beaches, runs between Hamilton and Dockyard). The Aquarium, Swizzle Inn, and Shelly Beach (popular with the locals) are along the #10 and #11 routes. If you are coming from St. George and want to go to the south shore beaches (Horseshoe Bay, Warwick Long Bay, Elbow Beach, for example), transfer buses in Hamilton -- it's very easy as there is one large bus terminal there that is well marked.
Here is a great map that I found very helpful in planning: MAP
. This map (as well as the bus and ferry schedules) will be available at the visitor's centers, and perhaps onboard, yet I found it very useful to have it in advance, even though I have visited before.
One important thing that we did not realize -- bring more cash than you think you will need as bus passes and most museum admissions must be paid for with cash only -- no credit or debit cards.
Hope this helps start with your planning. I'm happy to answer other questions.