I've done my figures, and I estimate the following b.p.h. in the a.m. peak at its busiest hour in Oxford Street:-
Marble Arch to Gloucester Place = 149 bph in each direction, total 298 bph
Baker Street to John Lewis = 130 bph in each direction, total 260 bph
P.M. peak figures aren't too much different, probably 4 or 5 bph fewer in each direction. Between peaks take off around another 10 bph from these figures and you'll see why, other than for running time, peak extras on London buses are by no means universal on all routes, or even the majority these days.
Comparable figures for, say, 2002 i.e. when most of these routes were still Routemaster operated would, in my estimation have been around 330 and 290 total for the two sections, since when conscious efforts have been made to reduce bus emissions in Oxford Street.