I agree with OFL. Even on a cycled 1 gallon you would still need two water changes a week.
The recommended tank size for a betta is 2.5 gallons, anything smaller and your looking at multiple water changes a week just because of the amount of ammonia the fish naturally produces.
Do you know what cycling is? You can go to our Betta Habitats section and look at the sticky on cycling. If you buy a test kit and are prepared to do a lot of water changes you can cycle the tank. Until you cycle I would recommend two 50% water changes and one 100% water change a week.
Here's a thread
on how to cycle with the fish in the tank as opposed to cycling before getting the fish that may also be helpful.