How do we know that Lady Catherine and Caroline BIngley are prejudiced towards Elizabeth? Are there any quotes to support this?
In addition to the previous information, we also know that Lady Catherine de Bourgh is the aunt of Mr. Darcy, and that she had already planned a bride for him with class, pedigree and money and that was none other than her own daughter, Miss de Bourgh. That is reason enough to detest Elizabeth after hearing word that Darcy wanted to propose to her.
On the other hand, Caroline was in love with Darcy and always kind of saw herself being married to him. She felt that she was the natural choice for him to marry, and she conducted herself at all times with the attitude of one who is in need to make someone fall in love with her rapidly. For this reason, knowing his interest in Elizabeth, both women detested her.
Lady Catherine's overall attitude towards Elizabeth shows that she is prejudiced against Elizabeth. During Elizabeth's first dinner in the Rosings, Lady Catherine continually inquires about Elizabeth's family and background, asking straightforward questions about her education and financial situation, such as "5 girls without a governor!" and "I believe Mr. Collins inherits your father's property."
Caroline Bingley's prejudice against Elizabeth is better hidden, nevertheless evident from the readers' perspective. When Elizabeth visits Netherfields for the first time, Caroline harshly criticizes Elizabeth's ruthlessness of walking all the way, wondering out loud whether Elizabeth's manners were properly taught.