Hi Carsten,
last year I crossed the Firth of Forth by the road bridge which has a good bicylce lane and provides a very nice view on the rail bridge. I continued on the bike route to Edinburgh which runs next to the A90 and is one of the worst bicycle lanes I've ever seen even in GB where the road maintenance people seem to hate cyclists. Parts of that lane had been grown over with bushes so you need a cutlass to get through with your bike.
I suppose that the A8 should be allowed to cyclists because it is not an M road or there should be marked an alternative bike route. If I was you, I would go to Scotland by ferry, not by plane. Amsterdam-Newcastle is quite unexpensive, for example, and you can avoid the risk of getting your bike wrecked when they throw it on the airplane.
Good luck,
Daniel