*Bowls = any container smaller then 2.5 gallons, without filtration or proper temperature, in any shape.
Includes vases, pots, and "betta" kits.

Can a betta live in a bowl?

Yes.

Should a betta live in a bowl?

Probably not!

Without anthropomorphizing the fish, it is difficult to explain. Imagine living in a small closet. You have room to turn around in, but no space to run or exercise. There are few things to look at in your closet, because there is no space to put decorations. You rely solely on others to bring you food and clean your "home."

• If your home is cleaned daily, you're probably fine. Extremely bored, but alive.
• If you have to sit in your own waste for weeks at a time or more, you're probably going to be miserable and even get sick.

So, yes, a betta can live in a bowl if you clean it and change the water every day. The bowl should have a heater and a thermometer so you can make sure the temperature is comfortable. The bowl should have silk or live plants so the betta can hide and swim around them.
It's going to be a lot of work and although the fish will live, it may not be thriving.

Fish of all species, no matter how small, are much more active and healthy then fish who live in bowls*.

We should not anthropomorphize our pets, or any animal in general, but we can safely assume a fish in an appropriately sized tank is happier then any fish in a bowl.

Refer to Tanks for more information.