I've read Jane Austen's Persuasion many times, but it was only recently that I read this passage and puzzled over it.
Anne...hastened forward to the White Hart, to see again the friends and companions of the last autumn, with an eagerness of goodwill which many associations contributed to form. They found Mrs. Musgrove and her daughter within, and by themselves, and Anne had the kindest welcome from each. Henrietta was exactly in that state of recently improved views, of fresh-formed happiness, which made her full of regard and interest for everybody she had ever liked before at all; and Mrs. Musgrove's real affection had been won by her usefulness when they were in distress. It was a heartiness, and a warmth, and a sincerity which Anne delighted in the more, from the sad want of such blessings at home. She was intreated to give them as much of her time as possible, invited for every day and all day long, or rather claimed as a part of the family; and, in return, she naturally fell into all her wonted ways of attention and assistance, and on Charles's leaving them together, was listening to Mrs. Musgrove's history of Louisa, and to Henrietta's of herself, giving opinions on business, and recommendations to shops; with intervals of every help which Mary required, from altering her ribbon to settling her accounts, from finding her keys, and assorting her trinkets, to trying to convince her that she was not ill-used by anybody; which Mary, well amused as she generally was, in her station at a window overlooking the entrance to the Pump Room, could not but have her moments of imagining.
The part that puzzled me was about the White Hart and the fact that Mary could stand at the window and see the entrance to the Pump Room. The only White Hart I know in Bath is in Widcombe, but nowhere near the Pump Room. After a little further investigation I discovered that there had been a White Hart Coaching Inn situated opposite the Pump Room in Stall Street. It was a major coaching inn - Charles Dickens also makes mention of it in Pickwick Papers.
And at seven o'clock p.m. Mr. Pickwick and his friends, and Mr. Dowler and his wife, respectively retired to their private sitting-rooms at the White Hart Hotel, opposite the Great Pump Room, Bath, the waiters, from their costume, might be mistaken for Westminster boys, only they destroy the illusion by behaving themselves much better.
Not only was this building eventually demolished but the Grand Pump Room Hotel which replaced it was also pulled down in1958/9 to be replaced by shops. I found this really interesting site with lots of images of Bath from the past Click here to see Bath in Time.
Another wonderful site is Bath360 If you click the link you can see what the Pump Rooms look like today - the White Hart and Grand Hotel are shops today, which can be glimpsed through the colonnade.