Welcome to the forum! ^-^
Well, really, it depends what kind of bowl you're using. I have a 2 gallon bowl that I keep one of my boys in w/ a heater (I don't use filters) and he's perfectly fine.
Generally, pet-store bowls are very small (half-gallons to one gallons) and that's a bit small, in my opinion, for a betta. In a small bowl, there isn't much room to swim around in or hide anywhere, really.
I know quite a few people that have biOrbs, though I've never used them myself or read up on them. Bettas are not very strong swimmers, so the circulation of water in a biOrb doesn't really matter unless you change the water as often as you need to. I have twelve tanks (one of them a five gallon) each with a betta inside, and I don't use any filters whatsoever. BiOrbs should be absolutely fine- as long as they're a 2 gallon minimum (some people would say 1 gallon, but that's just my opinion.) Be aware, they are hard to clean! I helped my friend clean out hers and it took a while.
And yes, as weluvbettas has mentioned, they are quite expensive. A regular 2 gallon and up tank would cost less.