Don't offer transfer unless you want to create additional work/cost for you. Having access to a credit/debit card is generally accepted as a minimum barrier to make purchases on line.
You usually only see CC and Paypal because workflows exist for making these payment pathways as easy as possible for the vendor. The providers charge a fee for this ease of use, but you just pay your fee and the money shows up in your account.
The rules and regulations for transferring money between accounts, however, are not the same, and vary from region to region. My experience is that payments can take different amounts of time, as can refunds.
Not everyone has Paypal, but Paypal presents a framework for providing the same transfer service you describe, and it's free to get an account.
Stick with the standard CC and Paypal options and if someone really wants to transfer from a bank account, they can sign up for Paypal.
If you're really concerned about this type of customer, you could add messaging to your site: If you need to transfer from a bank account, sign up for a free Paypal account".