What are the differences that could keep Mr. Darcy and Elizabeth and Mr. Bingley and Jane apart?

Darcy and Bingley are from a different class than Elizabeth and Jane. Darcy is from the landed gentry, and Bingley is from the successful business class. Elizabeth and Jane, on the other hand, are from the middle class, and their family does not have a great deal of money. In Regency England, when the book takes place, wealthy men (particularly men from a higher class such as Darcy) were expected to marry women within their class. These marriages were seen as the proper way for people to pair off, and they were also ways to keep money flowing into the upper classes.
In addition, the Bennett family does not seem like the appropriate kind of family for a man like Darcy to marry into. In today's terms, Mrs. Bennet seems tacky and ill mannered, and Elizabeth's and Jane's sisters, such as Kitty and Lydia, flirt with soldiers in a most unrefined way. When Lydia runs off with Wickham without being married to him, her act has the potential to bring shame to the entire Bennet family until Darcy arranges the marriage between Lydia and Wickham. Darcy is better suited to Caroline Bingley than to Elizabeth, as Caroline has money and has been raised to be upper class, but in the end, Darcy marries Elizabeth for love. Bingley also marries Jane for romantic reasons.