The costume was Helena's during the first part of NML when she was patrolling as both Huntress and "Batgirl". The mouth-covering was so that her identity wouldn't be spoiled (she got sprayed with paint in the face one night) when she changed out of one costume into another.
Batman basically took the costume from Helena (after admonishing her for failing), and handed it to Cassandra. How a mid-20s Italian woman has the same frame as a teenage Asian girl, I don't know.