That'd do it. Where does he have to swim in a wall bowl. Even bearing in mind that bettas aren't particularly smart fish, there's just not enough there to stimulate hime, so he'll hang out and eventually die of boredom. There's an annoying thread around about betta tank sizes. Annoying because everyone has a different opinion of the minimum size tank a betta can live in and no one is going to have their mind changed. Relatively pointless too because a betta can live in a tank only slightly bigger than it is.
The real question is the minimum size tank a betta can thrive in, and that's about 5 gallons. Frankly, even that is a bit small - I notice a definite difference in activity level between the betta I have in a 5.5 and the one I have in a 10.
So look, if you want a happy, healthy betta that will look its best and patrol it's tank, spring for a 10 gallon. Put in a heater and a filter (one that you can current kill - I like Duetto 50's.) and take out your filter carbon and replace it with peat or extra biological or mechanical media.
If you just want a betta that sits there looking glum you don't need to do anything. So long as you keep up with the water changes, he'll live for a year or 2.