I've never shipped my bike, but a friend of mine does every year for RAGRBAI (in Iowa, he lives in Georgia). He's done it 11 years or something crazy, and last year was the first year he had a problem. UPS lost it temporarily. Which gave him a major heart attack. But they found it and got it to its destination in time for him to do the ride, but barely. I think it showed up the morning we left for the start town. A lot of the guys on my team for RAGBRAI ship their bikes. You can rent one of those cases from your LBS for like $40 or something similar.
Good luck
"Only the meek get pinched, the bold survive"