How would you go about asking out a girl who is selective and doesn’t like unwanted attention?

We are new friends and I think I’d like a relationship with her at some time. She asks me personal questions about what I would want in a women etc, and I’ve asked her personal questions like if a person was willing to expect her flaws would she feel better about her self. She is willing to tell me personal things and vice versa. She has stayed that she is not interested in people getting in bed with her and so dresses down and is selective with whom she spends time with. Lately she has asked me to go to the gym with her, and I excited to go with her. Im terrible at reading women do I have a chance with her? Who’s would you proceed with the relationship?

How would you go about asking out a girl who is selective and doesn’t like unwanted attention?
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