What zip code 4 do I enter to add the card to bank bill-pay

You should be aware that using a bank’s bill-payment service is considered a “non-conforming” payment method under the terms of the AppleCard agreement.

As such, it may, or may not be accepted. Or it may be accepted but not be posted in a timely manner.

The agreed-to methods are at Related Article link.

Apple Card agreement is available here:

https://www.goldmansachs.com/terms-and-conditions/Apple-Card-Customer-Agreement.pdf

Do you mean using your card for recurring payments? Yours.

Or, are you trying to enable auto payment of your Apple Card? Add your bank in the Wallet (Open Wallet > Select Apple Card > Tap "more," (the three dots). Tap Bank Accounts to add your bank. Review Scheduled payments to set up automatic payments. Otherwise, you simply pay in the Wallet.