It is my understanding that at a formal ball or assembly you should not dance with your siblings. (This is mentioned in Emma).

So therefore, Miss Bingly could not dance with her brother, Mr. Bingley. And Mr. Hurst being married to Miss Bingley's sister, he would also be called her brother. Would she also not be able to dance with him? In which case, if Mr. Darcy did not come, she would have no one in her party to dance with if the company was completely unsupportable.

Is it possible that Mr. Darcy was forced to attend in order to entertain Miss Bingley at least for two dances? In the end he only danced with her once, but perhaps the company was not as poor as expected? Or she was more in demand than expected?

Mr. Darcy danced only once with Mrs. Hurst and once with Miss Bingley, declined being introduced to any other lady, and spent the rest of the evening in walking about the room, speaking occasionally to one of his own party.