Why do girls ignore the guy the like?

I've been seeing this girl at my gym for about 4,5 month. She looked interested and caugh her looking from time to time then I decided to approach her. I waited for her to finish her workout and I kinda introduced my self and asked her about her workout. After that i tried to talk to her again but she avoid me and everytime we come across she tries to ignore. Now she doesn't avoid me completely like she's still looking from time to time mostly from far and she seems to be fine working out around me but everytime we come across she tries not to look at me. Now I feel she is a little shy and she gets nervous around me. Now I really like her and wanted to ask her out but not sure how. Any suggestions.