You could always try to ask questions to gauge how open-minded she is.
Last year I was roommates with a very conservative Christian, and I was terrified she'd freak out when she found out I'm gay. Turns out, she was perfectly fine with it.

So, you never know.
You could always throw out a statement.. I don't know, mention something in the media. Something like "Have you heard of that transwoman on America's Next Top Model? What do you think, I think she's pretty." And see what her reaction is. If it's one of disgust or disbelief, well, you have more of an idea of where to go from there, while still not putting yourself in any danger just yet.

And if she says something like "yeah, she is pretty," then you know she at least doesn't have a
problem with it.. which makes it much more likely she'll be fine with having a trans roommate.