I once moved a bike with a bike trailer. It wasn't much fun, but you could make it work. I have also moved wheelsets and various parts, forks. I haven't moved a full frame on a bike though and even the wheelset barely fit on the rear rack.
One trick that does work is to move the bike on the city's buses front rack. Works pretty good if it is a complete bike.
Another time I bought a frame and fork and brought it aboard the bus. Driver never complained..