Hi Ryan,
It may be more of a personal feeling on your end that this girl tends to pass by you no matter where you sit.
If the both of you are constantly in the same space, it is always likely that you will see her pass by you.
Hence, this is more coincidental than anything else.
However, she does appear to be a socially awkward girl, as she tends to be alone and acts strange whenever you both bump into each other even though you believe that she is fully aware of who you are.
Being that she is most likely a socially awkward girl or a girl with social anxiety, all the staring that you have experienced from her in the lecture halls and at the library may be simply due to curiosity. In essence, she may be a people watcher by nature.
If she isn’t the kind to socialize all that often with people, she may be the kind who would much rather look at people and try to figure out what they are all about.
This allows her to still maintain a comfortable distance from them due to her social anxiety while still being able to make herself believe that she knows them to an extent.
She may or may not be interested in you.
She is probably the type who hasn’t even allowed herself to truly acknowledge whether the curiosity she has for you is merely out of habit because she is a people watcher or out of romantic interest.
It may be best that you just come right out and ask her out.
Since she is always alone, it wouldn’t be hard for you to come over to her and do this. This way, you can truly determine whether there is any potential for romance with her without wasting any more time trying to figure out whether she likes you or not.