Some LDT's insurers like to know beforehand. There is usually an option on the entry forms although it might be possible on the day, worth a phone call to the organiser.
Haven't done an LDT for a while but seem to remember it being around a tenner for bikes.
It was possible on the Moor to Sea, however the regs for the 10 Tors did not have an option for day insurance as I recall. The secretary of the Meeting may be able to help. I will PM her number to you.