first, and easiest way to fill your bottle is from the tap. The water on board is all filtered and safe to drink and does not have salt in it as some people fear.
Or, at the Ocean view you can get all the water you want, although they do ask you not to refill your container directly. Fill a glass, and then transfer from that glass to your contact. (They want to avoid having your container possibly touch the spigot. )
Otherwise it just takes a moment to get a bottle (or can, or carton) of water at Cafe al Bacio or any other bar.
and finally, yes you can bring a case of water on board with you which might make sense if you have no beverage package.