I made something like that for bringing my bike on the train when I lived in Europe. I haven't used it in the US though. I made it out of a couple of super-cheap fleece blankets, a long zipper, some velcro, some buckles, and a couple of long pieces of webbing. The bike went in upside down with the handlebars turned and the wheels off, and the wheels went in big pockets on either side. It took only a few minutes to pack and unpack and was light and compact enough to carry in my saddlebag on a ride. It was easy to carry and worked well.
I wouldn't try checking the bike as airline luggage that way, though. And I haven't tried it on Amtrak in the US - they seem to be much more uptight about not letting people clog up the trains with gigantic suitcases, even though their checked luggage system (where it exists at all) really sucks. It would probably work well on a bus, provided that you can pay attention to how stuff gets packed in with it, and it would probably work on public transit or commuter trains.