Caroline Bingley is a total mean girl. She's a lot like she is in Jane Austen's original: she's wealthy, she's ambitious, and she totally has the hots for Mr. Darcy. Only difference? Here, she can't behead a zombie to save her life.
Caroline and her siblings were never trained in the deadly arts, and, basically because of that, she thinks they're not such a big deal:
"If I may mention so delicate a subject, endeavour to check Miss Bennet's unladylike affinity for guns, and swords, and exercise, and all those silly things best left to men or ladies of low breeding." (10.31)
If you ask Caroline Bingley, slaying zombies just isn't ladylike. Yeah, but—that's mostly because she can't do it. In fact, she rips Elizabeth every chance she gets, just so that she can get in better with Mr. Darcy. Trouble is, we're not sure her flirting game is as good as she thinks it is.
Mr. Darcy is a highly trained zombie killer, so there's not much chance this line of attack is gonna work with him. He seems to like his ladies with a little blood on their hands. And Caroline is a lady with pretty much nothing on her hands…except maybe claws?
Did we mention that Mr. Darcy also regularly insults Caroline to her face? He sure does:
"Miss Bingley, the groans of a hundred unmentionables would be more pleasing to my ears than one more word from your mouth. Were you not otherwise agreeable, I should be forced to remove your tongue with my saber." (10.14)
It's time to get a clue, girl. Mr. Darcy is just not that into you.