If you're on a budget and willing to give it a go, the Number Eleven begins at Liverpool Street and takes in the Bank of England, St Pauls Cathedral, Fleet street, The Strand, Trafalgar Square, Whitehall, Number 10 Downing Street, the Houses of Parliament and Westminster Abbey. From there, it passes near to Buckingham Palace and you can get off and forget about all those nasty bus smells with a nice walk in the park.
So why not give it a bash? At least you'll be able to tell all those Big Bus Tour people thrusting leaflets in your face to p*ss off. For more information on central London bus routes, visit http://www.tfl.gov.uk/assets/downloads/central_bus_map.pdf, or for something a bit more twee, see this old post about heritage routes 9 and 15.