If there is to be a bus, especially if it's a free bus, perhaps Carlisle airport or Loganair could advertise the fact on their website and provide some details about this ? Expecting potential passengers to phone the airport to get details of the bus is not sensible.
As someone who lives near London, I'm thinking of buying a ticket on the Carlisle-Southend route but am put off by the idea that without details of any public transport start date or schedule, a 10 mile taxi trip to Carlisle centre will probably be in the region of £30 each way, making the train look rather more appealing instead