Mizter T gurgled happily, sounding much like they
were saying:

The webpage specifically says:
"Storage of cycles is only available for rail season ticket holders."

Which is perhaps a little ambiguous, because there aren't any rail- only
season tickets available for journeys on Chiltern from/to stations
shared with the Metropolitan line (i.e. Chalfont and Latimer), only
Travelcard seasons. The intention however is fairly clear - they are for
the use of Chiltern passengers.

Thinking about it, I seem to recall that bikes are required to carry some
kind of permit - bikes without a current permit gain a snottygram then,
presumably, disappear.

If you've got an LU season (even a weekly) that covers a Chiltern-served
station, I can't see how they could claim "rail season ticket holders"
didn't include you - at least, without any additional Ts&Cs, which almost
certainly do exist somewhere.