Oregon wrote:
You need to have them become comfortable with you being in their "space". Human contact, even a little goes a long way. Become a gentleman, help her on with her coat. Offer your hand to help her get out of a sunken beanbag chair. Carry heavy things for her.. even if they are not very heavy.
If you want to get into her space, you need to sneak in there

I do all those things already, but not for the purpose of "getting in there", but because I try my hardest to be a gentleman... I would offer help to move heavy things or holding doors for
anyone, regardless of gender (although the coat thing is a little more intimate than the other things you mentioned, and it would be hard to rationalize that one away, so I don't do that)... And I don't do anything with the the idea that doing such things will "get me something", I do it becaus it's the right thing to do...
I think that's part of why I make friends easily... but translating that into interest is next to impossible...