How would you approach a person that you saw only in passing but wanted to get to know better?

Here’s my example:
I take the train to and from work everyday. There is a woman I have seen twice within the last two weeks who makes me feel an intense attraction. We seem to be on the same schedule. After seeing her a second time, I deiced that if I see her a third time on the train (which is statistically improbable) that I’d at least like to introduce myself. What I have noticed in passing is that she has no wedding ring. Having no familiarity with this woman aside from seeing her on the train twice, it is potentially awkward to make any advance on what is for all intents and purposes, a complete stranger. How would you approach the situation of introducing yourself in a spontaneous fashion? I understand that asking this question here immediately renders any such interaction as anything but spontaneous.