How can I pay my taxes with a bank account instead of pre-paid debit card

[Critter-3]

If you mean your federal balance due then in the FILE tab choose to mail in a payment (then ignore the voucher) and pay directly online at  www.IRS.gov/payments and pick the direct pay option. 

[Opus 17]

To pay your TAXES with a bank account, you can enter the account number in Turbotax when you go to the File interview.  It will ask how you want to pay and if you select bank account, it will ask for the account number and routing number.  Or, you can select "I will pay by mail" and then you can make a payment on your own at www.irs.gov/payments.

If you are asking how to pay your TURBOTAX FEES, then I think customer support can take a bank account number instead of a credit or debit card, but you have to call customer support directly.