If you'd keep the betta in a bowl, you'd have to change water a few times a week since it won't cycle. Just a small amount, like fantailer said, roughly 20-30%.
A betta does need space though. If you count it as 2 liters per 1 cm of fish, a betta needs a 14-15 liter tank/bowl
There are those baby Biorbs available, they're 15 liters and have a little undergravel filter
You can also buy a small heater for those systems (planning on getting one for a future betta). Here's a link: (Link is not visible to guests. Please register to view.
You can find these for pretty varying prices, but in case you find a used one, be sure to inspect it for scratches! These tanks are made from acrylic, so they get scratched much easier than glass and being full of scratches they won't look too attractive