What is the Apple Card zip code where payments are mailed?

Whatever Zip code you provided as part of your address when applying for the Apple Card.

You can follow the steps here to find the Billing address for your Apple Card: link-> Update your Apple Card account information - Apple Support

there is this also

(I posted this because I am not sure that paying through your bank like that will be permitted)

Set up scheduled payments for Apple Card

1. Open the Wallet app on your iPhone and tap Apple Card.
2. Tap the more button , tap Scheduled Payments, then tap Continue.
3. Tap Pay My Bill to pay your previous monthly balance or tap Pay Different Amount to choose an amount. Then tap next:

• • If you chose Pay My Bill, select when you want your payment to be made, then tap Next.
  • If you chose Pay Different Amount, select your payment amount, when you want the payment to repeat, when you want the first payment to be made, then tap Next.

1. Confirm with Face ID, Touch ID, or passcode.
2. Tap Done.

If you want to change your scheduled payment, you need to first cancel your current scheduled payment. Just tap the more button , then tap your scheduled payment under Scheduled Payments. Tap Cancel Payments and tap Cancel Payments again to confirm your choice.