"they were dances of mortification"
Public Domain"Dos à Dos -- Accidents in Quadrille Dancing", 1817 caricature - Credit: George Cruikshank

Balls and dances where almost the only place where young men and women could meet and talk "alone". It was also the best place to find a suitor and was usually the prelude to any marriage proposal.

That's why to be stuck with a bad dancer and a young man who did not interest her was so trying for Elizabeth.