It's not even necessary to have a bank account with the same company that you have a credit card with. So your bank account is not linked to your credit card. You still need a convenient way to pay off your credit card, like electronic payments from your account to your credit card or whatever works for you.
* at least this is how it works in Canada, but for whatever reason we seem to be ahead of the US in terms of credit card technology based on what I've been reading (no pin? no tap payments? You still need signatures? Wtf?)