Regular cold water will do just fine. They don't need aquarium heaters, but they do like it to be anywhere from 65-72 degrees. 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". Overall, tap and well water is the best for bettas. 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. Basically, don't used bottled water. Tap water is fine. If unsure of quality, bring a sample to a pet-store and ask.