Yes, bettas can survive in a bowl. They're such popular 'bowl fish' because in addition to their gills, they can breathe air from the surface through their mouths.
That's why some pet stores sell them in tiny little cups...

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Personally I think keeping them in tiny 'traditional' fish bowls is pretty cruel, but there are nice big bowls out there, mine lives in a 5 gallon.
Good luck!