Perhaps a bus with a smaller turning circle than the current buses,
enabling them to move quickly arround the narrow London streets without
causing major blockages to multiple lanes, and in the case of bendy
buses, and even the normal ones.

Perhaps you could somehow segregate the driver from passangers, as in
trains, allowing the driver to concentrate fully on the road instead of
checking tickets? Maybe a guard could be employed, as on trains, to
check and sell tickets, and assist passangers (which the driver can't
do)?

If you can't afford a guard on every bus, have a "buy before boarding"
policy, and enforce with RPIs like on the trains and bendy buses that
we have.

does anyone know of a bus that would fill those requirements?

Sounds like the monstrosity of the Ftr that's running in York -
http://www.goftr.com/.
http://en.wikipedia.org/wiki/Ftr.
--
The presence of this signature shows that this message has been scanned
for misplaced apostrophes by the common sense scanner. However, some
apostrophes may not be included where required due to boredom, gross
negligence, budget cuts, incompetence, stupidity or just plain laziness.
http://www.railwaysonline.co.uk