This is a very old and hoary question that has been circulated around the vintage and classic movement for years.
Are the show organisers implying you are responsible for anything that occurs involving your bike whilst it is in their care and under their control? How can you be? What security arrangements do they have to ensure your bike is carefully looked after?. Are they not required to have their own public liability insurance policy covering their show? Lots of nasty questions to consider isn't there.
The response many years ago was that entrants should merely cross out that part of the entry form relating to public liability and initial the crossing out. If the organisers won't accept that then you don't want to know them.
Of course even if you don't want to ride the bike on the road it is probably sensible to insure it. It has a value as do your other possessions even if it is never on the road.
Sorry to be so unhelpful but insurance can be a minefield and everyones circumstances are unique. If I was you I'd talk to an insurance broker.
Cheers,
