I just wanted to mention this because the makers of P&P2, P&P3, and "Lost in Austen" irritated me by getting it all wrong! ;-)
*Miss Bingley* is the one who originally invites Jane to Netherfield, who also invites Elizabeth to stay, and is their official hostess throughout. When Mrs. Bennet comes to visit, even though Bingley is very anxious to keep Jane at Netherfield till she is better, he still exclaims "My sister, I am sure, will not hear of her removal," whereapon Caroline reassures Mrs. Bennet that Jane will have every care while she is with them.
I can see why the film-makers would skip this step. They would want to underline Bingley's niceness plus his feelings for Jane, while emphasizing Caroline's chilliness, but I'm convinced that in that era, Bingley as a single man would have no business inviting any single young ladies to his house (even for the best of reasons), just as Bingley, when he first arrived, could not meet any ladies until the gentleman had visited him, and *had their visits returned*. Also, neither Bingley nor Darcy would have any excuse to be anywhere *near* Jane's sickroom! (grrr ;-)