。
She's never even been asked out, you know.
Literal
She [topic-は] even-once date [for-に] was-invited thing doesn't-exist [you know-のよ].
誘われる is the passive of 誘う ('to invite, ask out'); デートに誘う specifically means 'to ask out on a date.' Combined with the experiential ~たことがない, the frame becomes 'has never been invited (on a date) even once.' The clause-final のよ is a feminine combination: の (explanatory) + よ (assertive emphasis), softening the assertion while still pushing the information at the listener. のよ feels conversational and mildly gossipy — exactly the right register for sympathetically (or unkindly) reporting on someone's romantic history. デート is a fully naturalized loanword, often verbed as デートする ('to go on a date').