Since your cruise ship will be docking at the Kings Wharf, a convenient dive operator would be the Blue Water Divers. They are the longest PADI operation in the island. They have a dive center at Somerset Bridge (at Robinson's Marina) which is about 10 minutes by bus from the dockyard. Bus #7 and 8 have stops right at the dockyard and you can take either of them to reach the dive center.
The afternoon 1-tank dive that starts at 1:30pm usually takes the divers to shallow wrecks and reefs. There are plenty of shallow wrecks at the western end of Bermuda. By the way, just to let you know that Kings Wharf is not an island. It's a berth or a pier where the cruise ship docks and located at the Royal Naval Dockyard. The dockyard is located at the western end of the island in a parish known as Sandys.
I suggest that you call up Blue Water Divers or write to them to get details about dives and courses offered by them currently. You will get their contacts here:
Hope this helps. Have a great time in Bermuda.