Researching for the Schools section, I've come across a couple places that expect you to submit an application for a credit card FIRST in order to pay for school under the (ridiculous) guise that "if you don't qualify for a credit card you don't meet the credit standards (background check) for CDL school." This is NOT what the rules state or even imply. Don't get taken by a credit card scam!
Your credit history is an open book to the trucking companies once you get your CDL. You do NOT have to have great, good, average or "need a co-signer" credit to get into a school or be hired. It helps. They will look at what you've gone in debt for. A company that requires truck leases may not take you with multiple bankruptcies, period. Those that hire company drivers may.
Any school shold be asking about your background before they even mention the "$$$" words. A paid-for CDL school will let you in with lousy credit before they'll take you with violent felonies, multiple DUIs or drug convictions.
Some schools accept credit cards for payment; this is quite different from requiring you to fill out a credit card application or REQUIRING you to use a credit card. Some questionable practices offer you a huge discount to use a credit card; if they offer you a larger discount to pay with a credit card than to pay cash it should be a real question of "shady."
If you have to apply for or give a credit card BEFORE they talk to you about school itself: Run like hell was at your back- it is.
And do not fill out an application until you know who/what you're applying to! If one reputable school will take you, any of them would. Choose the school, or 2 or 3 schools, tops, then submit your application. Each time they check your credit, it does count and can lower your credit score.