So this happened about 10 minutes ago. I was on the train (peak hour, going home after work) and this girl runs to the doors and asks if the train goes to a certain stop, then another stop, both of which I answered yes. She jumps on, thanks me and all I was thinking was, "she is pretty as fuck".

So I sort of carry on with the question she had asked, and said "so you asked about two different suburbs, are you lost or something?" as a joke. She smiles and tells me she's going to the first one but either one works for her. I joked that the train doesn't actually go to either station and now she'd have to get off at the next stop so I can guide her to the right one. She laughs and I maintain eye contact while tapping her on the shoulder saying "just kiddiiinnggg". I notice her blush quickly and look down then look back up to me. Good signs. We continue the conversation for another 10 mins or so.

By this point however, the whole carriage was eavesdropping, looking at us and I even saw some giggling. I didn't mind this but she definitely did because as soon as she noticed it, she became extremely closed. Start using the phone, looking away and using the pole as a barrier (as in she turned in a way so that the pole was in between us two). Eventually next stop I got off the train to allow other people on/off and when I got back on she was gone, assuming she found a seat or something.

Now as beautiful as she was, I'm not really disappointed but it got me thinking, how would you guys handle it? What could I have done better? Or is it just unfortunate circumstances?

The train journey to my stop (hers was after mine) was approx 25 minutes so I was pacing the escalation accordingly. In hindsight, maybe I should have been aware of the circumstances and sort of asked for her number/set up a future date quicker. What do you guys think/recommend?

BTW, I haven't done a cold approach yet but this is my first time talking to a new girl in daytime and it went much better than expected so I'm still bubbling about the experience :)