Hello Suba Pete,
I was looking into this very matter earlier in the year. I decided that I would go for the type of hard, rectangular gun case that is approved for transporting firearms by airline.
I didnt like the idea of walking with a gunslip in public, simply because it looks gun-shaped, and all too obvious.
I found some very useful information on the Metropolitan Police Web site about firearms, I suggest that you have a look at your local forces site, as Scottish law may well be different.
I did read that one is supposed to seek written permission to transport a firearm by train, from the railway company, but couldnt find any information about transportation of a firearm by bus.
The Met say that it must be transported in a secured case, I interpret this as a case that has locks on it, and nothing less than that. And I did read of someone being prosecuted for carrying a loaded firearm in a public place, when the individual was stopped by a police officer and it was found that a piece of cleaning cloth had been left in the barrel of the air rifle!
The Home Office makes a document available named Firearms Law Guidence for the Police 2002, it can be downloaded as a PDF. Its an interesting read (as is The Anti-Social Behaviour Act 2003), although I dont recall it dealing specifically with transportation, only storage of firearms.
If in any doubt, contact your local Firearms Enquiry Team for advice.
Hope this helps.
Merry Chrimbo
Paul.