Is there any place where I can find the geographically accurate route followed by a specified bus route in London?
Have you tried TFL's bus map webpage?
Bus Maps by City Area
You can also view maps interactively from the site. Zoom in to view the bus stops, click on the bus stop you need, and zoom out to see the bus routes. Below is a screenshot for the routes passing via Trafalgar Square stop 'T':
Bus Spider Maps
Finally, the website allows you to search for and download bus spider maps. You can search for the individual bus line, or by borough. Below is what the spider map of the 222 at Heathrow Airport North looks like: