In Jane Austen's Pride and Prejudice, is Miss Bingley speaking of Elizabeth's independence and spirit when she refers to "that little something, bordering on conceit and impertinence"?
And, if I may mention so delicate a subject, endeavour to check that little something, bordering on conceit and impertinence, which your lady possesses. (Ch. 10, Vol. 1)
Yes, in a way Miss Bingley is speaking of Elizabeth's free spirit and independent mind. What she means when she speaks of Elizabeth's conceit can be easily seen in a passage just above this one. Elizabeth responds to Darcy's question if she wanted to dance a reel by stating:
Oh!...I heard you before; but I could not immediately determine what to say in reply. You wanted me, I know, to say "Yes," that you might have the pleasure of despising my taste; but I always delight in overthrowing those kind of schemes, and cheating a person of their premeditated contempt. I have therefore made up my mind to tell you that I do not want to dance a reel at all -- and now despise me if you dare. (Ch. 10, Vol. 1)
In this passage, we see that not only does Elizabeth make assumptions, she has a very high opinion of her ability to discern a situation, and she even has a high opinion of her wit. She assumed a motive for Darcy asking her about dancing and responded in a very ironic manner.
This response is also an example of impertinence. In order for her to respond to Darcy in such a way, she assumes that she stands in a place in society that allows her to do so. Miss Bingley sees Darcy as being socially above her, which is true, considering who his family members are. Therefore, it is socially unacceptable, or rude, or impertinent for Elizabeth to joke with Darcy.
However, since the reader sees Elizabeth in a brighter light than Miss Bingley, what Miss Bingley sees as conceit and impertinence, the reader can see as freedom of spirit and independence of mind.