This is kind of a long shot I suppose but I don't know of another place to ask and Edinburgh Airport's own website isn't much help, with precisely one occurrence of the word 'motorbike' in the entire site.
Does anyone know if there is any dedicated parking for motorbikes at the place? I've seen one out of date anecdote that there was a bit near the Customer Services building where one could park for free, and a slightly less out of date anecdote that that ruse no longer worked. Another anecdote said you now had to pay for parking but it was cheaper than for cars.
I'm doing an audit/inspection there tomorrow, once the evening rush hour has passed, and I fancied a break from cycling!