Bettas are a pretty forgiving fish, water-quality-wise. While they do not respond well to temperature fluctuations, they can handle your tap water pretty adeptly. You only need to dechlorinate it, by using a prepared dechlorinator, or by letting the water sit out overnight to "de-fume". I added a link to PetSmart's Bowl Fizzies, below, for super-easy dechlorinating tablets.
Overall, tap and well water is the best for bettas and other aquarium fish - if it is safe for you to drink, then your fish can use it too. If you are unsure about your water quality, bring a sample to Petsmart or your local fish store for a free water test to make sure, and ask their opinion.
Bottled, filtered water is too sterile for pet fish. Your fish need the minerals present in natural water, just like you need sunlight to make and process Vitamin D. So save your money and drink the bottled water yourself! You can spoil your fish in other ways, like buying them special live food treats or new toys to swim under.
