What a coincidence. I was just looking up information on shipping bikes.
Generally, it costs around $35.00 to ship bikes within the USA via UPS.
The following was posted by "Cal" on www.oldroads.com
On March 20 2001.
1) Alway use bike boxes (available for free from your local bike shop)
2) Use 2 boxes per bike. One box to put the bike in and the other for cardboard packing
3) Remove the pedals and seat and wrap them in newspaper and put them in a plasic bag. Tie this bag to the frame.
4) Remove the wheels and the fenders. Then bolt the fenders back on to the wheels.
5) Remove the handlebars and stem, and wrap them in newspaper and place in plastic bag. Tie the bag to the frame.
6) Cut out the bottom of your 'donor' box and place it in the bottom of your 'shipping' box.
7) Cut an end off the donor box, and place it in a l-shape in the bottom of the shipping box.
8) Place the frame into the shipping box, placing the front forks on this l-shaped piece.
9) Cut one big side panel of the donor box and place it inside the shipping box next to the frame.
10) Cut about 20 4" x 4" squares using the narrow side sections of the donor box. Punch a hole in the center of each square. Jam these on the ends of the wheel axles to make sure the axles are covered in cardbaord.
11) Place each wheel/fender combo in the shipping box next to the cardboard you inserted in step 9
12) Cut up the remaining large side panel of the donor box into 12" x 12" and larger squares, and double up the protection at any point where the parts might come in contact with eachother.
13) Use tons of packing tape when sealing up the box. It is cheap and your local Staples store has the best deal on packing tape.