I don’t know what to tell you other than that’s impossible and/or your test readings are not accurate
Like I said before, this is going to be an expensive and labour intensive hobby if you have to buy and lug around water all the time. Once the tank is cycled and all is well, you still need to do weekly water changes or at least semi-weekly. An ro system may be your better option long term, but you will need to remineralize the water or you’ll have a whole new issue on your hands!
With an uncycled tank it can definitely seem like you’re steadily changing water trying to drop the ammonia. I personally wouldn’t get excited if the test showed 1ppm as that’s a fairly acceptable level for most water parameters. You also have to consider the fact that it’s just a home test, it’s not bang-on accurate and sometimes it’s hard to differentiate the readings. But at a 1ppm reading I would do a water change or plan to do it soon (in your case next day if you had to go get water)
Did you happen to check your bottled water again to make sure it didn’t have trace amounts of ammonia?