Did you have to provide your own bike box at REI? The reason I ask is that REI has told me that unlike most bike shops where each new bike is shipped individually to the store in a cardboard box, with REI the bikes are shipped on their truck from their distribution center to the store partially assembled. So according to REI, they don't have the "typical" cardboard box that we would need.
I've also shipped a bike via Amtrak. That is cheap, and the nice thing about that is the boxes are huge, so you only have to remove the handlebars and pedals.