The fact that it's a bowl isn't the problem, if you can filter and heat it then it's a round aquarium, and if it holds a couple of gallons of water then it can sustain some level of cycle and stability. But then you have something like a baby Bi-Orb, OK for a betta or a handful of tiny fish. Shrimp and snails are of course a good option for a smaller tank.
But the question is Why? It's probably going to cost more than a standard 10 gal tank, and is not going to work as well.
I have a 2 gallon jar planted, which holds a few gold white clouds in the winter. Seems every summer someone gives me their unwanted betta, which houses the betta until I rehome it. This jar has only ambient light (sun room w/sky lights) and no heater. The anubus has doubled in size in a little over a year. Bad pic below: