If it were me, I would have turned the music on or called a friend and not played into it. At my age, that behavior doesn't fly and turns me off fast.
Upon dropping her off, I'd say "It's clear you're not talking to me for reasons I'm unaware of. If you change your mind and want to clue me in, you know how to reach me."
And leave it at that. Do not call, do not contact, and certainly find a more mature woman to spend your valuable time with.
Your other options are to play into it and pick at her until she tells you what's up her a$$, or get angry, be defensive, be apologetic, be supplicating, etc etc.
Others might differ in their approach, but standing your ground in the face of such immature and abusive behavior is non-negotiable. Hope this helps, let us know what happens!