A blue stocking is a woman with pretensions to being intellectual. It is an uncomplimentary term because it implies a degree of pretentiousness. It is applied only to women. I'd suggest it's a somewhat old-fashioned term. It's a word I'd expect to hear in intellectual and academic circles.
▶noun often derogatory an intellectual or literary woman. word history: A bluestocking was originally a man wearing casual grey-blue worsted (instead of formal black silk) stockings. Later the word was used in reference to those who attended literary parties held around 1750 by three London society ladies, where some of the men wore informal dress. The women who attended became known as blue-stocking ladies or blue-stockingers.