You need to be using dechlorinater with both the tap water and bottled water-some bottled water is just filtered tap water and it still can contain the additives to make it safe to drink
To switch over-use 50/50 tap/bottled along with the dechlorinater-on your next 50% water changes use 100% dechlorinated tap-on the next 100% water change use 100% dechlorinated tap water
On 1gal unfiltered tanks I recommend-1-50% and 1-100% weekly water changes to maintain water quality
On the 50% water change use a clean plastic up and dip out half the water and replace with like temp dechlorinated water
On the 100%-net the fish and place in a small container with some tank water-pour out the tank water-rinse with warm tap water-fill with like temp dechlorinated water
Pour half the water out of the small container with the Betta and fill with some of the fresh new tank water over 5 minutes-repeat....then net the Betta and place in the tank and top off with fresh dechlorinated water of like temp
Important to monitor water temp and try and keep it within a few degrees between new and old water to prevent temp related issues and to use dechlorinator with any water added to the fish.....