yeah the line “if your into that sort of thing” doesnt exactly work since its more of a takeaway.
A fun get to know you question would’ve been good, or any question which you can demonstrate high value in.
i would just say “our romantic date of course” as a next response.

The date line is fine but I would have said "where are you from" after she said nice. Best to leave "if you are into that sort of thing" after you said something escalating and she didn't reply to it