Get to know a girl I see every day

Hi, this is probably my first and last post here but I would like to know your opinion and get some advices. Please don’t judge me to hard… so I’m going to the gym almost every day, and there is a personal trainer who is working there, and she is very beautiful and positive. We had some eye contact and she smiled to me, so I smiled back a few times (I know it probably does not mean anything. But I would like to get to know here somehow, and I was thinking to book her so she can train me and start like that, However I don’t want it to seems that I’m using those sessions to just to “pick” her up. So I’m wondering should just I go to her and speak and try to invite her for some date or get to know her first and then? I’m not ugly, good form but I’m afraid that the girl is not my league, anyhow. But I have quite good confidence. Hope you understand what I mean. Thanks 😊