A Klein bottle is a topological thingie, rather than a Euclidean geometry thingie. Given the nature of these beasts the sofa will be both inside and outside the bottle at the same time.

The sofa will need a pretty odd shape to not be able to move around the bottle - say a torus which is around the "handle" of the bottle. Any shape that does not snag the handle will of course be able to be moved around it as needed.