If you need to change the payment method on your DispatchBot account you must do so using the Admin account.  The admin account is generally the email address used when you signed up for DispatchBot.

Once logged in click on your name in the upper right corner and select "Administration"

On the "Administration" page select "Payment Methods"

It will list your current payment method for DispatchBot.  Click on "Add card" in the upper right.

On the "Add new payment method" screen enter your new card details and then click "Save and make this my default payment method".