I had originally intended to use this 13th century B.C. image of charioteers from Tiryns for the cover of Orestes: The Outcast, but the wear and tear on the fresco, and the unevenness of the checkered border made it unlikely.
There is a female counterpart of this image, in which a woman drives a chariot with her female friend as a passenger. So noblewomen could and did drive in those days.