Most people find that the water does have an odd taste if you're not used to it. I personally don't care for it, but I travel a lot, and I don't usually care for the water anywhere I travel. You get used to what you have at home.
Many people on here do think that the bottled water tastes fine, but I'm not one of them. The water they sell is Zephyrhills, and I don't like it at all, so we bring our own water. Disney policy allows guests to bring in water, so you won't have a problem there. We don't usually carry any extra bottles in. We always take at least one break, so I bring a new bottle each time we leave the hotel room. I carry large bottles with at least 3 servings (24 oz) of water, and we buy juice if we need anything extra to drink.