It'll be about $20. Get a used shipping box from a bike shop and break the bike down. Make sure you pad EVERYTHING that touches so there's no scratching going on during shipping. It's tough to get the bike parts arranged in the box just like they were from the factory, but it's important to avoid any damage.
1. Get a used bicycle box from a bike store.
2. Break down the bike. Take off the pedals, cranks, seat, wheels (duh). Take the handle bars out of the steer tube, either let them dangle or turn them sideways.
3. Throw foam padding between anything that could rub.
4. Zip tie wheels and handle bars if you so desire to the frame so they don't move around.
5. Either zip tie or packing tape the other miscellaneous parts to the frame or inside of box.
I don't know about shipping or things like that in the US. Shipping from points in Canada to points in Canada is $20 I think, so I would think it would be along the same lines in the States. It really shouldn't be an issue at all.