I know this isn't what you were asking, but you might consider bringing refillable water bottles with you instead of ordering bottled water. I did this last trip and it worked out really well. We used the ice and water from the soda machine in the QS at the resort, then refilled in the parks as necessary. There are a lot of water-bottle refilling stations at all the parks now and, incidentally, also at the airport.
I always used to get bottled water, as the tap water in Orlando is yick, but the water from the soda machines may or may not be filtered, but it tastes fine.