What you ran into is called "dimensional weight" which is basically a calculated minimum based on the size of the box.

When I need to ship a bike, I use FedEx ground, and carefully measure to make sure I don't exceed the dimensions that would trigger dimensional weight. You can sign up for a free account online and get a 10% discount on shipping. Then after you set up your shipment online, you can have them pick it up at your house or just drop it at Kinkos.