I never understood in Chapter LV why Jane was so distressed at her mother's attempts to empty the room of everyone but herself and Bingley. Why, if she wanted to get engaged to Bingley, did she want EB around?

The next day, the same thing happened except that this time, EB went to write a letter thinking that the rest would be playing cards-" she could not be wanted to counteract her mother's schemes".
Why didn't EB want Jane and Bingley together and alone? How did she think they were going to get engaged?
Did she not want to get engaged and then married?