How to approach a woman cold during work commute (female replies only)?

I think that you should become friends. If you are interested in her and want to get to know her outside the bus, then tell her you find her interesting and you would like to get to know her and ask her if she would like to go for a cup of coffee or hot chocolate. Give your number instead of asking for hers. I would not give my number out to someone I do not know and I would not if I didn't really know that person.