She won't hold eye contact?

Anonymous
There is this girl that I think is really pretty that I would like to talk to but I have this problem. I see her looking in my direction occasionally, but that is always from further away and I am never sure if she is looking at me or something else. However whenever I am close enough to actually make eye contact I will look at her waiting for her to look at me, but the second she makes eye contact with me, she will immediately look away. One day I am pretty certain she was looking at me and she smiled as she looked away and then later in the day she was training someone(she is a personal trainer) and they came and used the machine right in front of me and she seemed nervous.(combing her hair with her fingers, playing with the zipper on her jacket, etc) Well as she was walk away, she looked back at me, saw that I was already looking at her (I was also smiling because I was laughing at myself for something) and she immediately looked away. Anytime we are close enough to actually make eye contact and she catches me looking at her she immediately looks away, but I will then see her staring in my direction from further away, even if I glance over at her, she will keep staring. She acts shy, but she's not. I see her talking to pretty much everyone in there(guys or girls) but with me she won't hold eye contact for more than a half a second if we are within 25 feet of each other. Why is this?

SHORT VERSION:

Why will she stare in my direction from far away, but when she catches me looking at her at a closer distance, she looks away before I even have a chance to smile? She is not shy around anyone, except possibly me.
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+1 y
I would love to go up and talk to her, but She is never alone, and I am shy, so between her never being alone, and never holding eye contact, it makes it extremely difficult. If she was alone and I knew she wanted me to I probably could, but otherwise, not so much.
She won't hold eye contact?
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