I go to sport centre where I regularly see one girl (both of us are middle ~20's) that trains children and teaches them to skate.

I tried to meet her, so when I went past her in locker room, I said "Hi". She had her back turned to me in that moment (was packing her stuff to bag) and I noticed she had earphones, so I was standing next to her until she noticed me, then I smiled and said "Hi" again. She took off her earphones, smiled and said "Sorry I didnt hear you".

Then the conversation looked like this. During this part, I felt really calm, we were smiling and she seemed comfortable:

Me: Are you going to train?

She: Yes.

Me: I see you here often, so I thought I'd say hello.

She: Ooh yes, Hi. Sorry I didnt hear you, a lot of noise here and I was listening a song too.

After this, we got into elevator and thats where I started to be really nervous, forgot what I wanted to ask and started panicking.

Me: "Thats okay. Btw, what are you listening?"

She started to nervously look around, and then said: "I dont know, whatever."

Me: "So for example?"

Then she told me type of music and language of music. I found out she is not from my country so I asked where she is from, she told me and I said "Thats interesting, i hear no accent in your voice". I think she just nervously smiled. We got out of elevator, she saw parents of child she was going to train and went towards them.

I just contunued my walk. Then I realised i didnt introduce myself, so when I saw her to finish talk, I slowed and told her "So now we have met. Btw, I am [my name]." and gave her my hand.

She didnt understand (I have kinda hard name to understand) so she asked to repeat it. Told her again, she told me her name, gave me her hand, nodded with head and told "Nice to meet you".

After that, we just continued our ways.

I feel like a creep, because when we were in elevator, I was really nervous, then she started to feel nervous too, we stopped smiling. When she gave me her hand, she handed me just fingers. And we also didnt make eye contact since then, despite she met me again in lockers when I was about to going home (there are also toilets).

I saw her take and wait for the elevator, but it looked she kinda rushes here and didnt looked back. I was about to take elevator too, but didnt want her to feel anxious/uncomfortable she has to talk with me again, so i took stairs.

I just feel bad now, regret I started to be nervous. She has really good energy and I dont want her to feel discomfortable next time she sees me. Definetly wont make any conversation with her again, i know its already over.

I just want to be "safe person" and wonder how. I usually dont meet random girls, I dont know how to behave.