To make cold water last the whole day, put a couple bottles of water in the freezer the night before*. Naturally, they’ll all turn to bottles of ice. An hour into the day, after the ice melts a little, you have a nice cold drink of water. When you see a water fountain, you can add more water — or, add water from unfrozen bottles.
In most developed countries, tap water is as good (or better) than bottled. Plus it’s cheaper and greener (of course, it’s ok to use the same bottles over).
* Be sure NOT to insert FULL bottles into the freezer! They might explode or leak when they melt, if the bottle has cracked from the pressure.