It depends on the context. If you're talking about how much of it you drink,then it would be uncountable. If you're discussing brands, then it could be countable.
If I was carrying a bag containing seven bottles of mineral water, I would say "I've got a bag full of bottled water". In BrE, "bottled water" doesn't mean "water which has been put in a bottle". That could apply to tap water. It refers to commercially-available water which you buy already in the bottle. It is usually mineral water or spring water.
Drinking water is also used in some countries for bottled ordinary water that has undergone reverse osmosis and been treated with UV to make it drinkable, places where you really shouldn't go near the tap water.