Hey gymrat,
Good work on cold approaching a bombshell, congrats.
From your summary, your conversation with her on the train sounded formal, like a business interview, which is less than ideal. The frame needs to be that you are the prize. Imagine you were an aristocrat surveying your domain when you chanced across her. Something about her sparked your curiosity, so you deigned to talk to her (cred. Will_V). She needs to impress you. Now, of course, you shouldn't be rude or arrogant. But that is the frame.
You should get her to talk as much as possible, and emotionally stimulate her. She will experience different emotional states with you, and become more invested in getting to know you further. You can talk a bit about what you study or do for work but not in the usual superficial way. The purpose should be to connect with her. Pacing and leading her reality is also good.
Also, remember that, whereas women ARE value, because they give birth, men have to PROVE their value, in this life. This means that a 20-year-old guy is seen as less valuable than a 20 or 24-year-old woman because he still has to prove himself.
So, as empath suggested, either match her age or tell her you are older. Since you're not looking for anything serious, you don't need to tell her your real age.
Lastly, for arousal, I would stick to non-verbals like EC and incidental touch - so good job on the hand clasp and hug.
I don't think things are going anywhere with this girl. But with practice, I'm sure you will get the hang of this. I would download WhatsApp (the primary vehicle to interact with chicks) and use Instagram only as a supplement.