There has been hired a new gym receptionist. We haven't talked much besides 'hello' and 'good bye' but for some reason I feel like she might be interested because she always notices me when I walk by and always responds to my greetings. How do I take things further?

Next time you go there hit her with this

"OMG you're here AGAIN?!?! Stop stalking me you creeper!"

^^ something smartass like that is what I'd go with. Saying hi and bye and being nice to ppl is part of her job she says the same old boring greeting to how many ppl everyday? Make the way you address her stand out in a funny way that makes her laugh or at least smile then she'll remember you and you can carry on from there.

Give you an example. There's a hottie who works reception at my gym. I walk in one day last week and she's learning against the wall looking blasé playing with her hair.

Me: "Wow, don't you look all excited!"
Her: (smiled) "I'm bored blah blah blah" (I didn't really pay attention)

I had then asked her if the gym was closed tomorrow for Canada Day, to which she said no, they're only closed one day a year, xmas day. So I continue...

Me: "Ugh, that's ridiculous, what's a jew to do?!"
Her: (laughing and smiling) "Oh I don't know!"

I go on to ask if there's another gym (it's a gym chain) run by any jews so I can workout on Xmas.

So in that brief moment I shook her out of the monotony that is most people's lives. If anything but to bring a smile to her face, and some laughter - my demeanour is totally non-chalant/fuck it, there's no nervousness about me if she laughs that's fine if not that's fine too I'm entertaining myself. I wasn't outcome focused, you can clearly see, but now she'll remember me and I can easily build on this. I intentionally kept the interaction short as I had a workout to do and didn't want to linger trying to dig up something else to say because that wouldn't be natural for me.

In the past month I have found out she is indeed interested. Whenever I walk in the gym we always look each other in the eyes and maintain it for multiple seconds. However there was always distractions so I had an excuse of not making a move. Many times she was on her phone or having a chat with friends so I didn't want to interrupt her, but anyway we always looked at each other.
Today I had opportunity because she wasn't doing anything. As usual we maintained eye contact as I was approaching to collect locker keys. When I was there I didn't say anything, which is the mistake I made. I couldn't think of how to break the ice because we had never had any conversation and we don't know each other. I'm an introvert so all this 'getting to know each other' and shit aren't easy for me simply because I lack energy to do all of that. I could say that I'm too lazy to do it. It's like going against my own nature. My plan is to just say 'hi' (in my language 'hi' is what you say to friends and 'hello' is what you say to strangers if that makes sense) next time and see where it goes because I don't feel like I could do anything more at the moment. Can any fellow introvert PUA's could give me some advice on how to force myself to have a conversation? Additionally I lack motivation to do this because then I will have to deal with all the dating which will be exhausting for me. I feel like it's too much hassle to just get sex.