It's very easy to mis-read situations in daily life, and what you're talking about is far from daily life.
Perhaps Anne is nervous because you are 16 years younger than she is. Perhaps she is a bit envious of your youth and the NRE. Perhaps because of these things (or others I haven't thought of) she puts on a tough facade.
The only way you'll ever know is through communication. However, I certainly would not start out the conversation with "I know you don't like me; and I don't like you." I would try something far more diplomatic, along the lines of, "I notice we're kind of awkward around each other, and I wonder if there's something we could do to make us both more comfortable?" She may not respond right away, but if she is really just feeling insecure herself, you might be able to break through and turn it all around. While yes, there are people that are hard to get along with no matter what you do, probably a greater percentage of them just have the tough facade thing going and that can often be brought down. Underneath, often lies a relatively nice person, once their insecurities are laid to rest.