Lee,
As a fellow air gunner (and biker) I sympathise with your plight. However, in this regard I think discretion is definitely the better part of valour. Air rifles, like knives, are an emotive issue with the public at large - and even to some members of this forum (although less so with knives it would seem).
I would hope that no member here would deem it appropriate to browse the aisles at Sainsbury's with his or her full set of sharps hanging from their belts, similarly we have to be ultra discreet as an air rifle looks more like an offensive weapon than the hunting tool that it actually is.
Unfortunately for us - whatever case you put the rifle in looks like...well...a gun case. The hard plastic cases attached to military motorbikes are designed for the rifle 5.56 (or SA80) and will be too small for your purposes.
Unless you can invest in a take down rifle like the Air Arms S410 TDR which can be discreetly carried in a rucksack then my advice is do what I do - bite the bullet (no pun intended) and leave the bike at home. Transport the rifle to your shoot in the locked boot of a car and carry the written landowners permission on your person.
Ride safe and good shooting!
Fin