Keep your own database (Score 1)

While I still don't necessarily support requiring an iris check, the bank doesn't necessarily need to keep a database of iris patterns. The pattern just needs to be stored on the card registered in your name. An iris check would just involve the ATM matching your pattern to what's on the card. Thus, the card is still the key to the account, but only you can use the card.

This isn't a solution if you want the supposed "extra convenience" of just needing to flash your eye in a scanner to match to a database. A card match method does provide increased security, though.