Goan,
Penuyah in the time of the Gemara was a penuyah tehorah, i.e. not a Nidda. Nowadays our penuyos are all niddos and therefore the issur yichud is d’oraysa, just like an eshes ish. That being said, I don’t know why single girls would be worse, they should be the same.
On this topic generally, there is no halachic difference between going on a date and driving with someone of the opposite gender and giving them a ride outside of the dating context. If anything, the driving on the date has greater potential problems because of libo gas ba (after the first date or two) and because the context of dating lends itself to kalos rosh.