We always rent a car and do a shop at one of the local Publix stores near Disney. I should note that we stay in the Disney home away from home properties - full kitchens full-size fridge, etc. If you want to save some real money, eat at least one meal in your room.
Anyway, getting back to the water, we usually buy a couple of 6-packs of the sport-top type and several of the smaller 1/2 liter type, and a couple of gallons for the room. We do love the taste of that spring water, especially while walking around WDW on vacation!! Anyway, both mom and dad have the larger insulated bottle water holders, and each of the three kids have the smaller (1/2 liter) size insulated holders. We put a sport top on all three bottles, and you can even freeze them for the next day (don't forget to take some of the water out first and loosen the top before freezing).
Anyway, the tap water at Disney leaves much to be desired.