If you're looking for a place that sells fruit, making it possible for you to purchase bananas, then you'd ask "Where can I buy some bananas?" If you used "May I" in this context, it would imply that you needed permission to purchase the bananas.
When you make a deposit at a financial institution, it's "in the bank."
Ex: "I'm going to spend half of my paycheck on rent and groceries, and then I'm putting the rest of it in the bank."
- For Teachers