i see beautiful girls on the train all the time. I wonder what the best way to approach a girl on the tube without theme being startled

you've seen her many times and all time. going direct will look like you're hitting on her. situational openers, opinions or whatsover is good. just be casual, calm and cool. speak slowly and clearly with lots of pauses. don't be ashame to let her know about your intention i.e you want her but you don't need her, note: there's distinction between the 2 intentions i just mentioned. good luck!

_________________
A's Ranks Higher than King and Queen

I am in the same situation. On my commute to work, there is a blonde who I would rate as an 8 get on at the penultimate station.

I notice the first time she gets on, I get up and put an empty bottle in the bin (which she is standing in front of). She smiles. The next two or three mornings, I see her get on and get her attention. Every time she has smiled in a slightly shy way, not in a "why are you looking at me" way or just to be courteous.

Approaching is a bit difficult because the final station is 4 minutes travelling time and the train is busy by then. When we get off the train, we walk in separate directions.