Hydro Homies

Majority of the bottlers who are of notable size buy "blanks" which are heated, blown, and formed by equipment as part of the bottling process. Blanks are essentially the lip and cap portion of the bottle, but instead of a bottle below that it's a vial of plastic about 2 inches long and an inch wide. It's cheaper to ship blanks and blow them at the destination than it is to ship fully formed bottles. The benefit of this method is that the bottler can have their own bottle design, but buy blanks from any standard producer.

From blanks to formed bottles filled with water is literally fractions of a second the process happens so fast. It takes longer for the bottle to get a label and end up in packaging than it does to form and fill.

EDIT: Also, very few bottlers produce their own water. They use tap water from a large municipality and then additionally treat it to match brand specs (taste and flavor). If you drink Dasani or Aquafina you're essentially drinking tap water.