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Caroline doesn't want Jane to have anything to do with her brother because she considers her not "good enough" to marry into the family.
"Jane receives a letter from Caroline Bingley stating that they have all left Netherfield for town and have no intention of returning. She states that Mr. Bingley will most probably not return for at least another six months. The letter also speaks of the family's expectation that Mr. Bingley will marry Georgiana Darcy, implying that they do not want him to marry Jane. Elizabeth attempts to comfort Jane by reassuring her that Mr. Bingley really is attached to her and that in spite of his sisters' efforts to prevent him from marrying Jane he will most assuredly return to Netherfield.
By informing the reader of Bingley's departure only through the letter of Caroline Bingley, Austen leaves many details up to the speculation of the reader. The description of Jane and Bingley at the Netherfield Ball leaves little room for doubt as to their mutual regard. It seems clear, therefore, that without outside persuasion he would not simply leave Netherfield with no intention of returning in the near future. According to the letter, Mr. Bingley himself had only planned to be away from Netherfield for a few days to attend to someone business. It seems that Caroline and her sister, and perhaps Mr. Darcy as well, plan to follow him and to persuade him not to return at all. This scheme seems particularly likely considering that Mr. Darcy had overheard Mrs. Bennet's jubilant conversation at dinner regarding what she considered to be the imminent engagement of Jane and Bingley. Knowing how much Mr. Darcy is concerned with social status, it is not unlikely that he would try to persuade Mr. Bingley not to propose to Jane."