OK, this is how you get around the ones that want your bank account. H&R Block has a prepaid debit card that has a routing and account number. You can use it for direct deposits and withdrawals. I know this because I got blacklisted by ChekSystems because of a dispute from a bank that said I owed them money after I closed my account when I did not. I had a client who paid by direct deposit, so I started looking for alternatives. My roommate worked with H&R Block and told me about their card. I used it for two years until my ChekSystems ding cleared. No charge for cash reloads from your bank account, but it's pricey for cash reloads, up to $4.95 depending where you get it done. You can also transfer Amazon Payments and PayPal funds to it. An ATM withdrawal is $3.00, plus whatever the ATM charges, so I always just got cash back on something at a store. There is a small fee for monthly bill pay, but a regular monthly transaction is only 95 cents, so not bad. Expedited payments get pricey, though.
I never had any trouble with mine the whole time I had it. I even had to use it for my SS direct deposits until I could get a bank account, and it worked fine. I just paid my bills online using it as a debit card, or by money order.