On the first day on board, they offer a good price if you buy a case of bottled water and keep it in your cooler for the trip.
Also, the ship "makes" it's own water from evaporation of seawater. This is common on all large ships (experience in the US Navy), and the quality is excellent and purer than anything you will ever get through a tap on land.The only question would be if the water is treated with any chemicals, and if so, what and how much.