Do betta fish really need an air pump in their tank/bowl? Can they just sit in still water? And if they are in s5till water, how often do you have to change the water??

No, they do not need an air pump.
Beta fish breath through an organ called a labyrinth, it is comparable to our lungs.
They surface to the top of the water to breath in a gulp of air.

If you are planning to keep your beta in a small beta bowl, the water should be changed no less than every other day.
If you plan on keeping it in an aquarium or tank with a filter, then a partial monthly water change is all that's needed.