A lot of people are shy.. in polls, over 50% of the people in the USA call themselves shy. Every AFC has shyness, approach anxiety is related to shyness, and we all can identify with that. I personally think that a lot of people just portray this image of having friends.. having things to do on the weekends. However, a lot more than we think, at any age range, regularly spend weekends alone. I personally sarge alone all the time, and am only slowly building a circle of friends, and people say I'm very sociable. Now, if they're calling me sociable, and I have to deal with "loneliness", imagine others who are too paralyzed to put in the energy.
I basically agree with Ojete, but would use different words. Don't get drawn into her problems. You know very well you have to face your social anxieties for yourself. Let her own her shyness, or whatever it is.
However, if you feel good around her, by all means, keep that going! Your options are to keep things as they are.. saying hi at work. Or, you can grab a cup of coffee together, invite her to lunch when you go out with friends.. friendship kind of behavior. Or, if she passes your requirements, you can advance to more than friends.
Personally, if she's cool to be around, I'd at least invite her out to lunch with friends.. I can always use another friend.
