I see her frequently on campus and have had the opportunity to chat with her on occasion. Never about writing, however. Just small talk about the weather, events on campus, etc. I would love to take one of her writing seminars but they're not open to graduate students. If you had the chance to talk to her, what would you say?
Have you read any of her books? If yes, are there any issues connected to the books that you'd like to raise with her? Authors nearly always love talking about their books with somebody who has read them, so that's certainly an opener. But only if your interest is genuine, and you know enough about the book to sustain a conversation with the author about it. If you haven't read anything she's written, I'd just keep my head down and walk past, if I were you!
So...do you like oats? Sorry, it's just that everyone makes fun of my surname; now it's my turn! Seriously though, I haven't read any of her works, but any writer I meet, no matter who they are or how experienced they may be, I always ask them what books they are writing at the moment and how they go about writing it. I'm fascinated by the almost infinite amount of ways writers write.
I would probably ask her about her favorite books/authors. I love hearing about those sorts of things.
I would ask whether she really wrote that op/ed piece with her name and photo on it, currently online at The Onion.
With any writer I might meet, I'd be interested to know how they do things, simply because I like to see what options are out there to try. But having a read a couple articles she's written about writing, I'm not sure I'd go out of my way to engage her in discussion. She seems (and I may be wrong in my assessment) a bit too "There is The Way to do things and if you don't follow that, you'll fail.". People like that I'm not really interested in.
You don't want to ask a question whose answer can be readily found in a number of sources. For instance, a quick visit to Wikipedia tells us both how Oates writes (from 8 to 1 every day, and then a few hours in the evening) and who her biggest writing inspirations were. (Faulkner, Dostoevsky, Thoreau, Hemingway, C. and E. Bronte) You want to ask something different. A question she hasn't answered many times before. Having never read any of her works myself, however, I can't tell you what precisely that is!
If there was an opportunity for conversation about writing, I would compliment her on the short story she wrote for the Spring 2013 issue of Boulevard and ask her some questions about the ending.
