LOL I love bettas, too. They're such gorgeous fish! :icon_mrgr
In your shoes, I'd use a filter. You don't want a strong filter, as bettas don't like too much water movement. A tiny HOB (hang on back) like a Palm or Azoo would work, or a small sponge or in-tank filter... there's numerous filter options availabe for nano tanks these days. An established filter can really help maintain water quality. I'd be sure to include at least a little biomedia in the filter.
I'd plan to change 50% of the water each week if you get a filter.
If you don't get a filter, then you'll need to do water changes much more frequently, at least 2x-3x a week.
If you don't cycle the tank at all, I'd plan to change some water every day. About a gallon a day would ensure that the water stays good and clean, especially if you're conscientious about cleaning up any uneaten food (you can use a little airline tubing siphon for that). If you've got the tank stuffed with healthy live plants, you may get by with just 3x a week... except then the plants will suffer from lack of nutrients after a while.
Cycling the tank does make life easier in the long run.