How do I reciprocate interest in a woman that previously approached me?

Months ago a female gym bunny approached me at my gym, introduced me to herself and her friends, info-dumped on me and invited me to classes. As a shy guy I was hesitant; yet I followed through to join her for several classes. Due to work being tough I stopped going to the gym and lost contact. Now that I have returned to the gym, she is back in my orbit, and though she hasn't spoken to me she has walked beside me in public at my slow pace, smiled at me, shared gym rooms alone with me, etc. Is she gauging my interest? I previously suspected she was acting on behalf of a friend by being the courageous one to approach, but now I'm not so sure.

I know I am at fault for trying to hide my liking of her and her actions, and being perceived as aloof; I'm cautious to remain respectful and avoid crossing boundaries at the gym. Those that approach me are usually the sporty type, yet she was the first to approach me initiate social conversations on several occasions; but this is in the past. I'm certainly open to her if she communicates she is still interested next weekend. What do you think about the situation?

How do I reciprocate interest in a woman that previously approached me?
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