You have no proof that the error, if there was any, was made at the bank. Sadly, in this day and age, you can't trust the bank to be honest if you turn up there and say something along the lines of "I think we have $500 of your money". They'll take it and then wait for you to prove that it wasn't theirs.
For all you know, at this stage, some mysterious benefactor may have slipped an extra $500 into her pocket. Put the money aside and see who contacts you. Don't even mention it to anyone lest word gets back to the bank and they then contact you knowing that they can get an easy $500 profit out of you just by asking for it.
You clearly don't know for certain where the money came from so require clear evidence before parting with it.
Of course, if she left the bank knowing that they'd overpaid her to the tune of $500 then it's due for return.