Because they've now "been out together" she tends to
feel a lot more comfortable coming over.

I usually recommend that guys approach women, get their
email and number, and move on. You can get 5 or 10 emails
and numbers in an evening, and then have dates during the
week (where you don't have to deal with distractions,
competition, etc.).

But if you're at the point where you're confident in your
skills, and this is what you want, then try the technique I
just explained. I know more than one guy that uses it, and
it seems to be a big winner.