Yes you can, a fish tank will "cycle" over time with a fish in it. You said you read a bunch about cycling, but this proves that you probably just scanned over the information.
Also, please don't take this in a rude way, but you should really try to establish some sentence structures and punctuation in your posts so we can understand what you're trying to say. You say we jumped the gun, and that you had that fish tank 11 years ago. How are we supposed to know this, your posts are hard to even understand.
A Betta doesn't cost a lot of money, but they do require a heater, filter and a cycled tank. A bowl is not a healthy option for a Betta (or any fish for that matter)