I've heard that директор means "school principal" so we're really saying that the principal isn't at the bank now. Correct?
Yes, it’s a possible translation, but дире́ктор can be head not just in school, but also in other organisations.
Why is does "банк" change to "банку" here? I would have expected "банкі". Or does it have something to do with the declension type of the noun?