If you have access to the Deidre Le Faye book "Jane Austen: The World of Her Novels" there is a good discussion of sanitation during the Regency period in the section entitled "A Sense of Place." According to Le Faye, water closets (what we call "toilets") were becoming common in new houses from the beginning of the 19th century on, but chamber pots would still be in use in older homes to the end of the century. There were portable shower baths available by about 1810 (actually a hip bath or other small tub , a small water tank, a pipe and a bucket), but they were not common. It looked like Darcy's servant heated the water in the kitchen and carried it upstairs for his bath. I don't think it would be unusual, or embarrassing, for a servant to stay in the room to assist the master of the house or his guest. Our modern standards of privacy were not the norm in earlier times. There is much more detailed information available on the internet and in print on the subject of bathrooms throughout history.