Pretty good (and very quick) response from NMS *applause*:
"Dear Mr Robson
Thank you very much for your email. I admit we have not included information about travelling to the site via bicycle on the day of the Airshow and this is clearly an omission on our part for which I apologise. In reality we only have half a dozen or so cyclists each year for the Airshow, but this is no reason not to include the information, in fact such information might encourage others to cycle to the museum, which we firmly support.
On the day you will enter the Museum on the same route as all traffic, via the ticket desks at the runway entrances just off the B1347 (Just North of the Normal Museum entrance – if you travel toward the Merryhatton Garden Centre from Haddington). There will be lots of signposting on the day for you to follow. Once you present your tickets you can bring your bicycle onto the main museum site and lock it to the bike racks you noted next to our shop.
If you tell me where you are travelling from I will endeavour to provide you with an appropriate cycle route.
Incidentally, with reference to your penultimate comment, we pay a fairly substantial sum of money to hire the runway next to the museum for car parking and generally try our best to cover our costs. In reality, however, we do not make any money on car parking.
I hope this is helpful and apologise once again for the omission.
I look forward to hearing from you so we can try to plan a route for you."