Can I transfer money from my bank to Apple Pay

No, funding Apple Cash requires a debit card attached to a bank account. The only other way to add funds is give cash to a trusted friend or relative and ask them to send funds to you via Apple Cash.

Add money to Apple Cash - Apple Support

Send and receive money with Apple Cash - Apple Support

I don’t have debit card. Can I do the transfer from my mobile app to Apple wallet

Assuming that you mean to your AppleCash …

… YES, but only by using a debit card linked to your bank account AND which is also installed in Wallet.

See: Add money to Apple Cash - Apple Support