UK answer: You can get an account with basic facilities even with bad credit. The Halifax CardCash or Post Office basic bank account are good examples. You can't have an overdraft and get an Electron card only with these accounts. This means you can't spend more than you have.
A debit card shouldn't be a problem even with bad debt. You can only use what you have in the bank in the first place. A credit card however would be a problem. I suggest going into a bank (all of them if you have to) and talk to someone face to face about getting a debit card.
Do you mean a debit card or a credit card?
You don't need a debit card to pay bills and you can't afford to have a credit card if you are on benefits.
a DEBIT card comes with your bank account. if you want a CREDIT card and keep getting denied, try a secured card - you give $500 & have a $500 limit.
Go to the bank. Open a checking account.
Debit card comes with the account and transacts money in the account.