Where Melanie asks Scarlett to "help her" greet her guests. The idea was that Melanie had so many guests at her house for Ashley's party that she needed help attending to them all. I wonder if Mrs. Clay was that sort of help for the Elliots? Another thing I think, is that Mrs. Clay was needed as a companion for Elizabeth--after all E's not going to mingle with the lower classes, and it is not to be presumed that people who have spent the vast majority of their time in the country would have a great number of intimate aquaintance in Bath when they first arrive, so Mrs. Clay would be useful in that capacity. That is why, I presume, Mrs. Clay offered to bow out when Anne arrived. Anne can serve in those functions now.
Anyway, I doubt they truly did need her. It's just an excuse for Elizabeth to selfishly request the presence of her friend rather than her sister, whom she did not esteem.