Is there any other way to pay apple card bill than entering my bank account

No. You must pay with a bank account, either from the Wallet app or by going to https://card.apple.com.

I’ve been paying all of my credit cards online from my bank account for almost 20 years. Considering the current state of mail, it’s the only safe way.

If you are concerned about Goldman-Sachs having your banking information, remember that they (or any business) can get it from your credit history report anyway. But if you want to be really cautious open an online savings account with someone like American Express or Discover, and use that to pay the card bill and for no other purpose. Transfer money from your checking account into the savings account to cover each month’s bill.