ちゃわん or bowl in this sentence is not entirely correct. ちゃわん actually means rice bowl or cup. It is more common to use ボール for a single bowl.
I don't get it. What about a single rice bowl?
I assume @annamaeyasutani's point is that ちゃわん refers to a particular kind of bowl, and ボール refers to any kind of bowl. That said, ボール more often is used to mean "ball".
Google translate (fwiw) gives both bowl and ball as possible translations of ボール, but also suggests ボウル as a secondary translation for bowl. Might be worth keeping in mind.
"Give me a bowl please"
"I would like a bowl, please"
"A bowl, please"
"May I please have a bowl?"
Are all accurate translations.
"Can I get a bowl?" Is not
Would 鉢(はち)をください also work?
茶碗 --? Isn't this a cup (bowl) for drinking tea? That's how I've heard it used.