Hi Natalie,
That’s a good question. You can require that visitors become registered users on your site before they can make any purchases. That way they would be able to (and required to) log in again when they wanted to make another purchase.
I’m not positive about whether WooCommerce can save information such as a credit card number. Since the payment is handled exclusively via WooCommerce, I recommend that you check with them. They should be able to answer your question more positively than I could. Thank you!
Best,
Leah