Okay, fair enough. A couple of points just for interest:
Firstly, it must be admitted that we don't really know and much is assumed about Georgiana's residence. (also that it doesn't totally affect what Bingley did during the eight months in question) or affect the story too much. What we do know is that Bingley is an inmate in Darcy's house and Georgiana is there, whether from staying there or elsewhere in London. Re the establishment mentioned in the book, it refers to a year previously. Now, they are in London some twelve months after such establishment (which there is no argument happened, the book tells us so) was made/formed. During it, the unsavoury episode with Wickham occurred and Darcy would surely be very wary of any male attention to his sixteen year-old sister after that, (although he would presumably trust her to tell him of such) in making any further arrangements.. The initial plan was for them to meet in January (according to Caroline) and the Jane affair precipitated their plans somewhat. The rest is somewhat open to imagination and personal interpretation. Bingley's eight months must remain a mystery then.
Secondly: Derbyshire is a fair way from London ( 150 miles using Matlock as a reference) and in the age of stagecoaches would be time consuming and less than totally comfortable, and it does seem a little odd that Georgiana's education couldn't be conducted nearer to home, and that Darcy, a busy land-owner and not the most sociable person on the planet, should have a home so far from Pemberley just for the sake of London society. Really, considering her "little bit of ivory" statement of a few rural families, Jane Austen actually went quite far afield. (-:
