Bank should be able to give you $37k (amount financed) with you paying the balance directly to the dealer. Not sure what the issue is.
As an alternative, if you have a set amount you want to make as a down payment (ie $20k exactly) then you should be able to get a statement from the dealer listing the total sale price, less your down payment, equals amount that needs to be financed. Maybe just put your dealer in contact with the bank. It shouldn't be difficult.