The key to meeting a woman in a way that both you and her are comfortable with is to supplant need with desire, and to learn to approach meeting a stranger more intuitively. That is, let it happen naturally, never forcing it. Forcing it makes it uncomfortable for both sides.
In general, be fully engaged in the business of living your life to the fullest, serving your friends and loved ones, moving in positive directions, and you’ll naturally be attractive to others. You won’t ever need to force anything, because you’re happy with your life, though you’re always open to new possibilities.
Say you’re on the MRT (or standing in line at the bank, or buying something at 7-11, or jogging in the park). You’re single, available, not needy but open to whatever good things come your way. You see a nice looking woman. You glance at her, catching her gaze, and smile a little. If she doesn’t smile back, go back to what you were doing and don’t sweat it. You didn’t hurt anyone–you just smiled at someone is all. If she smiles back, then give her a little nod. If she keeps smiling and there is an empty seat next to you, you could wave to her as if to invite her to sit next to you, if that feels right. It might not feel right, in which case you just let it go as a nice, friendly encounter with a stranger. She might also refuse, which is okay too. Then you just smile graciously and go back to your own business.
The details of this kind of encounter will vary. The key is not to force it, to let it happen naturally. You want it too much, and everyone is embarrassed and uncomfortable.