I have a (well two now actually) Groundeffect bodybag. A slightly smaller model than the tardis. I can pack my bike away by removing the seat, front wheel, and drop bars.
I can leave my front and rear rack on (and you would get away with turning the handlebars sideways if you had flat bars. Then i can pack all the rest of my gear around the bike to protect it (not a padded bag, but it fairly hard wearing).
Has carry handles and a shoulder strap, folds down to approx A4 size and 5cm thick. Not sure on the weight, but isnt much