But if she expects any depth of feeling or keeps trying to get me to "open up," we're gonna have some problems. How do I tell her that?

Good question. I'd go low-key and minimalist. If she brings it up again, you can say something simple like: "I'm good. This is just me being me. That's all."
If she pushes again... "As I said before, that's not something I need to do. I'm not going to discuss this further."
If she continues to push, she has revealed herself as someone who does not respect boundaries. I would step back at that point.

If she enjoys drama, perhaps she'll grow bored of your lack of "opening up?" How long have you known her? Think of the man she's currently drawn to....messy divorce, technically still married. Perhaps she is hoping you will "open up" to provide her with some gossip and excitement?