We are looking for a way that patients can fill out their credit card information on a form and securely send it to our billing staff to run on our en

Unfortunately, it's not possible to collect credit card details through plain text fields, this activity is considered as phishing as per our terms: https://www.jotform.com/help/8-Terms-of-Use

You can only collect payments through our payment processing apps, here is a guide about it: https://www.jotform.com/help/323-Mastering-Payment-Form-Integrations-with-JotForm 

Thanks.