I started a new job a few months ago. Most days I see a HB9 on the train on my way to or home from work. It's always random when I see her so I don't think she works a typical 9 to 5 job like me. She gets on the train somewhere before me and stays on after my stop. Normally I have no problem approaching girls anywhere no matter the place and I would approach her no problem but there's a huge obstacle getting in my way. She always sits in the "silent" or "do not disturb" part of the train. In these sections there is no talking to the people around you or on the phone, and no disturbing or bothering the people around you (meaning no interacting with anyone) So it's not like I can show her a message on my phone or start a game of tic-tack-toe. These rules are very strictly enforced and those who don't follow can be kicked off the train, fined or banned.

I want to approach but I don't want to get banned because I need the train to get to work as driving is too expensive and there is too much traffic in the downtown core. And I can't just stay on the train to see where she gets off because then I'll be late getting to work. I was thinking I could either ride the train and see where she gets off on my way home, or take the train on a day when I'm off and follow her off the train then (although this could fail because her time on the train is always random) Does anyone have any ideas on how/when I can approach in this situation? And what I could say when I do?

Following her seems like a good idea. In a creepy serial killer kind of way. But still, could yeild some results.

Alternatives: Intercept her at the door or corridor. Or try using your phone to scan for her active bluetooth or wi-fi and send her a message. If she's into the "secret admirer" thing, you may peek her interest and get her to respond, if not, no one knows who you are.

As for what to say, I am not good at cold approaches and I am sure there are guys here much more qualified than me to help you.

As much as I want to I can't stop her before she is getting off the train because there is no corridor, the doors for entry and entry and so we would still be in the "do not disturb car". Plus even if it wasn't I wouldn't be able to talk to her because the doors are only open for about 10 seconds and I imagine she would get pissed off at me if I made her miss her stop by stopping her or blocking the doors. Either that or she would ignore me and just exit anyway. When I say follow her that was a bad choice of words I don't mean like a serial killer obviously. I just mean I would get off at the same stop as her and try to find a way to interact with her. I'm just not sure how to do this.

I think getting off at her stop is the only option. Once off, tell her 'someone told me there was an X around here that's why I'm getting off but I don't know exactly where it is, where is it.' If you don't give her a reason why you got off at her stop she will possibly think you are stalking since she has most likely noticed you on the train before. During the convo you can say, 'I think i've seen you on the train before' etc. and do your normal approach routine or whatever.

OR could go direct and say "I think you're cute but i didn't want to get thrown in jail for talking to you in the do not disturb section..." Then tease her with "look @ all the trouble you made me go thru i'm so far away from home now."

It's WAY more elegant and more likely to get her talking to go indirect though, as in the 1st pgf. of this post.