Why do girls usually hide their feelings?

I've been seeing this girl at my gym for about 8 months. She looked interested and caugh her looking from time to time then I decided to approach her about a month ago. 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 avoided me. I decided to just let it go but I feel that she's still have feelings for me, like I still catch her looking and i think she is a little shy and doesn't know how to deal with the situation and I don't wanna push it but I really like her. Any suggestions.