Can I transfer money from my bank account to Apple Pay?

Did you see this link - Add money to Apple Cash - Apple Support

After you set up Apple Cash1, you can add money to your balance using the debit or prepaid cards2 that you already use with Apple Pay in Wallet. If you don’t already have one of these cards in Wallet, you need to add one before you can add money.

Here's how to add money:

1. Go to your card info:

• • iPhone: Open the Wallet app, tap your Apple Cash card, then tap . 
  • iPad: Open the Settings app, tap Wallet & Apple Pay, then tap your Apple Cash card.
  • Apple Watch: Use the steps for your iPhone.

1. Tap Add Money. 
2. Enter an amount. The minimum is $10.
3. Tap Add, then confirm the U.S. debit or prepaid card2 that you want to use to add money. To use a different debit or prepaid card, tap  next to your card, then choose a card. 
4. Confirm with Face ID, Touch ID, or passcode.

To make sure that your balance is updating, you need a cellular or Wi-Fi connection.

No, there is not.