How long does it usually take for money sent to you through Apple pay to appear in your bank?

It takes 1 to 3 business days according to the Apple Pay cash card terms and conditions published by Green Dot Bank, but note that when you receive money via Apple Pay it will never be automatically sent to your bank account. Instead, it will be deposited to your Apple Pay cash card, which you can use immediately to pay for purchases anywhere Apple Pay and Discover debit cards are accepted. If you prefer to send the money to your bank account, then you have to manually start the transfer from within the wallet app or from Settings>Wallet & Apple Pay. Then it will take the aforementioned 1 to 3 business days for the money to show up on your bank account.