There is a small beach called snorkel park just a short walk from the dock.There is also a tram that you can ride over for free. The only thing is it opens a little later and doesn't open at all if the weather is bad,
It's also very easy to take the pink public bus to horseshoe bay, there's no need to pay 50 dollars per person on Bermuda. The bus system is super easy and the worst thing that will happen if you get on the wrong one is you'll get a tour of the island.
I'm pretty sure all the buses that leave from king's wharf go past horseshoe bay.
They should have a 'beach talk' on the ship.