I work with this girl who I think has a crush on me - I've been catching her looking at me for months, which has led to a lot of awkward eye contact and not much else. I can deliberately refrain from turning my gaze towards her and I will see her looking out the corner of my eye, I've even seen her repositioning herself to get a better look at me.

The way I've described that makes it sound like I should be creeped out, but I think she's quite sweet and just very, very shy, probably due to acute social anxiety - I would like to see where this could go if I can ever get her to overcome it with me.

This is the problem, whenever I try to speak to her if it's not a one-word answer I get a quick and nervous sounding response, like she just wants out of the situation. I'm at a point now where I feel like I should stop trying because it may be literal torture for her.

Can any similarly shy/anxious women shed light on what is going on here? Is there anything I can do differently?

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Additional Relevant Info:

I see her talk to almost no one in work, this is why I believe she is probably suffering from crippling shyness/anxiety rather than specifically me making her nervous for one reason or another.

This is a stop-gap type job for us, not a career. We don't really have to be concerned about workplace relationships.

She is Muslim, and although she doesn't dress orthodoxically, it's certainly possible that her family expects her to find another Muslim boy and she intends to respect that.