Whether a case or a bottle of water... you do not want to be buying it from Disney or anywhere on property $$$$.
Ideas:
1) Get groceries delivered via Vons/Pavilions,
Amazon Prime Now, or Instacart.
2) Wonderland Liquors is a convenience store on Katella and is (long) walking distance from DLH. I have done the walk a few times and cut through the Disney parking lot south of DLH. Some have reported they were not allowed in parking lot by security; I just haven't had this issue. If you do have to walk around on the sidewalk, it's a long haul. I have wheeled an empty suitcase there, and brought back the goods to both DLH and GCH. This was the days before easy delivery, however. Wonderland also did deliveries in the past. That may or may not have gone away with CV, and the option below.
3) Drizly App - was bought by Uber in recent months. This is alcohol delivery service and I think they have sparkling water, but maybe not still.
4) Stop on the way to the hotel. Either Uber or taxi, drop into a grocery and out. It still should pencil over buying single bottles. DK Livery services (I think) used to do a free grocery stop, included in their towncar/limo service.
5) Take bottles into the park and refill them at the filtered water locations. You can search for where they are... several youtube videos about them.
