Calling someone old is not defending yourself. Politely telling her that it was none of her business would have been the mature way to defend yourself.
I doubt the woman turned around and asked her the question out of the blue. Probably trying to fit in instead, and tried to join the conversation.
Age is only a number, how we think and feel is what differentiates us between "young" and "old."
Step back and give yourself time to cool off if someone is bothering you. That lady is nothing compared to what you're going to have to deal with down the road. People will be yelling at you, calling you names you've only heard on tv, throwing things at you, and maybe worse if you're one of the unfortunate ones. Their family members will join and make your life miserable if you let them. And to top it all off management will expect you to deal with it with a smile on your face to help their "customer satisfaction" scores.
Good luck in school, keep a cool head, don't party too much, and study hard. And keep an eye out for those "old" students, their life experience will prove valuable to you if you get to know them.