Bottled water usually contains minerals (also needed for health), which causes the white dust, but maybe in a different concentrations than tap water. Distilled or demineralized water indeed eliminates the problem. You can buy it in stores, maybe in large supermarkets or maybe via Internet. But depending on how much water you need, it can be impractical to continuously having to buy, transport and store large amounts of water.
Ultrasonic humidifiers often contain a filter to eleminate white dust, but those small and simple filters are usually (by far) not sufficient enough to filter enough minerals to eliminate the problem.
A reverse osmosis system like this: Amazon.com can remove almost all minerals, enough to eliminate the problem. I have a similar one like this. But it does require some space, water connection to use it, and it produces fresh water slowely (and also produces dirt water via a separate output).
Another solution would be to buy a different type of humidifier, but it can be very difficult to compare humidifiers. Every type has its own drawbacks, like noise, power consumption, white dust, humidification capacity to humidfy the room etc.
Most people here have no problem getting Soolantra prescribed. It should be easier to get than something like topical antibiotics. But in case it’s difficult, than there is also an animal version containing the same active ingredient: ivermectin. See Does yours spread? for more info about this.