Olympia shuttle during BETT?

Yes, the exhibition service will operate - Weds-Fri.

I've heard (sorry, read) that they'd just pull another train and use it HSK-OLY. One of the Wimbledon trains if my mind isn't playing tricks on me, but wether it was an Edgware Road or a city train I don't know.

I assume that LU either don't think people will plan their journeys, turn up at Earls Court, see there's a train to Olympia and catch it - or are being crafty and playing at the "closure by stealth" game (i.e. make a service unattractive, weirdly timed, badly advertised and unreliable and nobody will use it which gives you a great excuse to withdraw it without looking bad).

I am quite prepared to be told this is a dumb suggestion - especially in view of the modern environment in comparison to when the lines west of Earl's Court were first opened.
Build a short District Line link between Olympia and Hammersmith so that either westbound Ealing or Richmond trains serve Olympia rather than West Kensington and Baron's Court.
That way Olympia gets permanent service not only providing interchange with London Overground services, but also providing interchange at West Brompton with the Wimbledon branch.
The Olympia "loop" might operate only until say 21:00 and maybe not at all on ordinary Sundays, but surely better than an occasional unpredictable shuttle.

The BETT website shows the District Line Exhibitions only service times and shows that a shuttle bus will also be available from Earl's Court (not sure of Operator)
tinyurl.com/7zztx2q