So I then went for a more informal approach. "Care for a date?" Which got the reply, "I'm far too busy to do the dating thing ... I would much rather travel by trains with my girly friends..."

I suspect that National Rail log every query to refine answers and that there have been quite a few people who have asked her out on a date over the years so they decided to come up with a smart answer. Very good.
Shame you couldn't reply back saying "well I like travelling by trains too." Get out of that one Lisa.