In some places like India, you can order “boiled water” even in a restaurant – they know visitors may have issues with water safe for locals. It should get you boiled and cooled water, or else options for water that is safe for visitors – filtered or otherwise purified water – since they would guess that’s why you’re asking. It should work to get your point across, and they can let you know what options are locally available. Even if it isn’t a known thing where you’re traveling, it should get you safe water once they figure out you really want your water boiled.
In other places you can order as a drink something like hot water with lemon, a different context for the same precaution – boiled water. This may be cheaper than bottled water, since tap water is cheap and need only be heated, though no guarantees.
Another possible alternative is fruit – fresh squeezed juice (it must be undiluted, so very fresh and/or prepared before your eyes) is generally safe, and in some countries widely available. Even if not, eating some fruit can help you need less water overall as you get moisture from the juices.
ps – remember to be wary of local ice, it can be made from not-visitor-safe water.