Where can you find a list of Bank identification numbers?

You must get the list from a private source.

The ABA is the official registrar:

American Bankers Association

1120 Connecticut Avenue Suite 500

Washington DC 20036

If you try to get the register (list) from them, they state:

"The Register is not available to the general public," and go on to state, "The Register is available only to those institutions that have issued cards in accordance with ISO/IEC 7812 Parts 1 and 2 and whose information appears in the Register; authorized block holders, Sponsoring Authorities and network providers."

Because you can't get the information from the ABA, there are a few companies that specialize in commercial data and they have these databases you can purchase.