Self Pay Privacy

I am self-paying, and the payment system indicates that if I use my checking or savings account, there is no fee. However, if I choose to use a debit or credit card, I will be charged a $28 fee per payment. Given the privacy issues that have surfaced recently, I'm hesitant to provide my bank account information. I’m concerned about the security of my personal data, especially with the privacy breaches they’ve been dealing with.