Why not use fountain water taps and your own stainless steel bottle or glass bottle?
You're not crossing Death Valley on a mule. You're riding to the mall in an air conditioned SUV.
Drink before you go. Find a water fountain. Heck, slurp out of the neighbor's garden hose. Why are people so fragile these days?
I once read a pretty good magazine article explaining that public water fountains are generally cleaner than most office water coolers. I don't remember all of the details, but in essence, it's because they are regularly inspected by professionals, and the water moving though the pipes to get to the fountain and then through the spigot reduces the chances of contamination. Unlike your office water cooler where the water sits around forever. We have to have a guy come out to de-funk our office water cooler every three months.
Amazingly, people have drunk from public water fountains for thousands of years and been just fine. Spend some time in Rome and watch hundreds of thousands of people drink from tens of thousands of public water fountains all day long, and amazingly the city hasn't been wiped out by the cooties.