You need three cards total: Anna's keycard, Antone's keycard, and He'li's keycard. (All keycards are located in a chest in the same building as their owner). When you have all three, go to the bank and mention 'withdrawal' ... Leave the conversation screen, go into your inventory, pick up Anna's keycard, and exit out of the inventory screen with the keycard still as your pointer. Give the keycard to Lorrac (the bank woman) and she'll open the elevator for you (you get the keycard back).
Take the elevator down. Antone's card opens the door on your immediate left (coming out of the elevator). Leaving Antone's vault, use He'li's keycard on the left and Anna's on the right. (If you use the wrong one, the keycard falls to the floor).
There are also three more doors (around the bend in the hall). The ones on the left and right can be opened by your rogue/ninja/bard and have some decent loot. The door at the far end of the vault area is guarded by a tough guardian golem - beware. Use blinding spells/powders. Sleep does not work on it.
-- Josh