Use your tap water with Prime, change 100% every 48 hours.
Prime will detoxify Ammonia temporarily (the 48 hours). You could just add more prime instead of changing the water, but a 1 gallon is very small and needs frequent water changes anyways.
The ammonia will still show in the test kits, because it is still there, but it is in a non-toxic form. Unfortunately there is no way to test specifically which form of ammonia, at home at least.
Edit: I should use this as an opportunity to put a plug in for buying a larger aquarium for your Betta, 5 gallon minimum. He'll be happier, healthier, you can cycle it, and you'll only have to do a partial water change once a week (once cycled).
Prime will detoxify Ammonia temporarily (the 48 hours). You could just add more prime instead of changing the water, but a 1 gallon is very small and needs frequent water changes anyways.
The ammonia will still show in the test kits, because it is still there, but it is in a non-toxic form. Unfortunately there is no way to test specifically which form of ammonia, at home at least.
Edit: I should use this as an opportunity to put a plug in for buying a larger aquarium for your Betta, 5 gallon minimum. He'll be happier, healthier, you can cycle it, and you'll only have to do a partial water change once a week (once cycled).