While it's possible to get a signature loan without a bank account, having one makes receiving funds much easier. Even if you know you can't get a bank account, you may still be able to get approved for a signature loan, depending on the lender's requirements.
Be aware that bad-credit signature loans may charge interest rates as high as your state's limits. In some areas, borrowers with credit challenges pay 30% APR or higher.
If you are able to get a bank account, it may be worth the effort to have easier and faster access to your loan funds.