When we made the move from North Carolina to Portland, OR, we both picked out one bike that we figured would work for the most situations (it was winter, so we picked good rain bikes) and we brought those bikes across the country with us on our car (we also drove to avoid putting two dogs and a cat on a plane in the winter).

Our stuff went into storage for months (including our 6 other bikes) and we lived with just one bike each for awhile. The bikes in storage went just as they were - no modifications. The moving company was very careful with them and we had no issues at all. We did not box them up - we just made sure to tell them how precious these bikes were to us and they kept an eye on them. I would be worried boxing them up that that would give them licence to be rough with them or to store them on the bottom of a huge pile of books or something. But I have also since recommended these movers to everyone I know - they did a fantastic job....and I've moved a lot in the past, so I've got a lot to compare them to!