As long as you do frequent water changes, it's not that bad not to have a filter, right? Deal is, my betta HATES water movement. He gets all panicky and such. Soon as I turned off the filter, he's instantly happy again. This is normal, I've heard, but I just want to make sure he'll still be able to be healthy :)
A filter is not necessary for bettas if you can maintain proper water quality without it. Other fish require surface agitation for the water to be properly oxygenated, but bettas can breath atmospheric air.
What are your water parameters? It really depends on the size of the tank, but if it's anything under 2.5 gallons, I would recommend doing daily 50% water changes, or at least that every other day. If your ammonia levels always remain at zero, you're doing just as good a job as a filter would.