Do you mean the Delta branded Business Platinum Amex card (vs. unbranded one which does not have a free checked bag benefit on Delta)? There's no need to purchase ticket with card or show card to get free checked bag benefit. You just need your Skymiles number on flight as Delta and Amex share information and Delta can see if you are a Delta Amex cardholder based on your Skymiles number. Having DL Skymiles number on flight is actually a requirement (simply showing Amex card is not sufficient because it could be cancelled).