This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
Most of the "body English" riders display is gratuitous gesturing,
much like the motorcyclists who stick their butt out in curves while
their bikes never get down to 45 degrees (the angle below which hiking
out becomes necessary to keep hardware from dragging on the road). In
fact, in a series of tight ess bends, there's no time to do any of
this. It's done by supporting weight on the (horizontally positioned)
pedals, and unless the road is rough, with a light load on the saddle.
On rough roads, the cheeks of the saddle, (the ones that went away
with the Flite like saddles) are used to hold the bicycle stably
between the legs while not sitting.
The path through a curve is not symmetrical for a bicycle, because it
can slow down much faster than it can regain speed. Thus the
trajectory is naturally asymmetric. Brakes are generally used to the
apex (that is usually not the middle) of the curve, where pedaling at
that lean angle is not possible, nor does pedaling accelerate as fast
as braking decelerates.