That is Clearwater Beach you linked too. It is not close to the Dockyard cruise port. Long Bay Beach is in Coopers Reserve. Both are on the other end of Bermuda from the cruise port at the Dockyard. Long Bay Beach is great but you have to go to Clearwater, walk into the reserve, then walk to Long Bay Beach. No vehicles are allowed in the reserve. There is a gate. There are no bathrooms like OP asked for. I have been there. Clearwater, Coopers Reserve and Long Bay Beach are about as far from the Dockyard cruise port as you can get. I did them when docked at the cruise port in St. George’s.