From my experience with uncycled tanks, 100% water changes are a must. This is why I prefer cycled tanks, because they're easier to maintain and you only have to do partial water changes once a week. However, since your tank is too small to cycle anyway, I suggest 100% water changes every other day. I also always suggest that you get a liquid ammonia test kit and test the water before a water change to make sure that your schedule is up to par (ammonia always needs to be at 0 ppm). With the test kit you may find that you only need to do water changes twice a week, and that may be fine, but you also may find out that they need to be done every other day.
Do you have a heater? Keeping the water at around 80 degrees is a must for a healthy betta.