Boxing a bike for shipping is a common service that pretty much all bikeshops perform. They will partially disassemble it and put it in a bike box in such a way that it hopefully doesn't get damaged during shipping.
You can save yourself ~$50 if you do it yourself. Check out Youtube. I'm sure somebody has an instructional video on how to do it.
A shipping guesstimate would be $55-$90 depending on how far you have to ship it. I have found Fedex ground to be cheaper than UPS ground for bikes.