Miss Bingley saw, or suspected enough to be jealous; and her great anxiety for the recovery of her dear friend Jane received some assistance from her desire of getting rid of Elizabeth.
Miss Bingley is jealous of the attention that she sees Elizabeth receiving from Darcy. This comes on Elizabeth’s second evening at Netherfield, at the end of “dancing a reel” scene, which has been preceded by some lively banter. Notice that Mr. Darcy does not always reply to Miss Bingley, and when he does his replies are curt. Once Elizabeth enters the conversation, very briefly in a short remark directed to Bingley, Darcy jumps in with both feet. I believe this to be another example of Darcy choosing to have conversation with Elizabeth, as we saw in Ch 8’s “accomplished women” discussion (my message 43413 below).
What is interesting to me here is that Miss Bingley, hoping to gain Darcy’s attention herself, notices what Elizabeth does not. Elizabeth could not help observing, as she turned over some music books that lay on the instrument, how frequently Mr. Darcy's eyes were fixed on her. She hardly knew how to suppose that she could be an object of admiration to so great a man; and yet that he should look at her because he disliked her was still more strange. She could only imagine, however, at last, that she drew his notice because there was a something about her more wrong and reprehensible, according to his ideas of right, than in any other person present. Elizabeth certainly has no reason to believe that Mr. Darcy finds her anything other than “tolerable,” which she knows for certain.
Miss Bingley, in observing his look, his conversation, and what might be considered, especially to Miss Bingley, the flirtatiousness of the “dancing a reel” exchange between Elizabeth and Darcy, correctly surmises his interest, because if such looks and conversation were directed at her, that is exactly how she would interpret them.