Henry wrote

Also, for some mysterious reason appears that this only calls at
Hampton Court _Station_ going towards Esher, but not on the
return journey.

Going towards Esher, the buses pull off into the station
forecourt, but on the way back the last official stop before
the Green (on the other side of the Thames) is Summer Road,
(by the level crossing).
That probably counts as walking distance if you're fit enough
to cross the road in mid-traffic to the station-side pavement
immediately; otherwise there's currently a couple of hundred
yards of mud slick and a couple of nasty junctions to negotiate
to reach the pelican crossing at the station.

The obvious solution would be to turn into the gyratory and
share the bay already used by buses heading along the riverbank,
but simply go right round and turn left back on to the bridge.

Probably unnecessary since there is already a stop for other buses to
Kingston just before they turn left on to the bridge (451,461)

Of course that would mean buses both to and (~hourly) from
Kingston sharing a stop, which no doubt violates some
incontestable diktat.

There are examples where even the same route number shares a stop in
opposite directions. In Surrey I know of examples at Walton station,
Cobham (Waitrose), Sunbury Tesco and in Byfleet. Is this a "double
teacup" ?

OTOH in Esher with three routes to Kingston the paths taken and the
one-way system result in the buses that use those routes leaving from
three different (and widely separated) stops.

--
Mike D