I admit being greatly amused by the nature of the first respondents when this question was posted — a question by a man, drawing comments initially from men.
And yet none of the men have pondered what idle young men of means in one of the world's largest cities might have done with free time amounting to eight months in Georgian/Regency/Edwardian or even Victorian England?
What would
you have done, gentlemen, in Bingley's shoes?
I don't think men have changed all that much in 200 years. Men of wealth without professions, whose time is not eaten up by requirements of wage earning, still occupy themselves in:
— sports (ex. Four Horse and other riding clubs, horse racing, Angelo's)
— gaming
— investment opportunities and subsequent management of same (ex. buying and selling of shares in businesses like East India Trading Co, business loans, buying into funds including the government's fund)
— events and venues (theater, opera, museums, art shows, festivals, etc.)
— socialization with other men (clubs like Brooks', White's, Boodle's, coffee houses, literary or merchants’ clubs)
— socialization with women (both public and private in nature), and in mixed sex environments (parties, balls, soirees
— politics where appropriate and where interest encourage (land holdings and capital-intensive investments would have been inducements)
The question becomes, what did these occupations look like during the estimated time frame, beyond the examples mentioned?
A young man of wealth could keep himself quite busy, especially if he was determined to lose himself in occupation.
As for whether Bingley stayed with Darcy: Caroline refers to Bingley as an "inmate" of Darcy's as noted in this thread, but it must have been common knowledge Bingley was staying with Darcy as Elizabeth makes a similar observation to her Aunt Gardiner.
Quote
Source: Chap. 25, Pride and Prejudice, Jane Austen
"I hope," added Mrs. Gardiner, "that no consideration with regard to this young man will influence her. We live in so different a part of town, all our connections are so different, and, as you well know, we go out so little, that it is very improbable that they should meet at all, unless he really comes to see her."
"And that is quite impossible; for he is now in the custody of his friend, and Mr. Darcy would no more suffer him to call on Jane in such a part of London! My dear aunt, how could you think of it? Mr. Darcy may perhaps have heard of such a place as Gracechurch Street, but he would hardly think a month's ablution enough to cleanse him from its impurities, were he once to enter it; and depend upon it, Mr. Bingley never stirs without him."
"In the custody" suggests Bingley is in residence at Darcy's townhouse, in my opinion, as does the implication the two men are nearly joined at the hip.
