Pride and Prejudice is a bildungsroman in the classical sense, and probably one of the earliest and most enduring English bildungsromans. Elizabeth Bennet is a successful bildungsroman heroine, successfully finding a balance between the independent and free development of her character and proper socialization into aristocratic British society. This is what makes Pride and Prejudice a classical bildungsroman.
Elizabeth Bennet shows an independent streak, doing thinks like rejecting Mr. Collins in marriage as she develops independent character, finding him an improper match, not only because she does not love him, but also because his behavior is often indecorous.
While her independent conscience grows during the novel, she also finds a balance with socialization through her successful marriage to Mr. Darcy. She must lose some of her pride and overcome her prejudice to submit to willingly submit to marriage to him. And he of course must overcome his pride and his prejudices against her before the marriage can occur.
All of this really represents the successful organization of society. The people have to submit to be governed, they must submit to socialization into society. They cannot simply do whatever they want in this vision of society, but they find harmonious balance between personal liberty and socialization.
Thus the bildungsroman genre allows Jane Austen here to represent a metaphor for a popular Liberal (in the classical sense of the word, not the contemporary) vision of the arrangement of society through the development of Elizabeth Bennet.