I've used UPS (most company's use them for orders under 6 or so units) a dozen times personally and lots of time for customers bikes, with good results. It costs about $80 to ship to Cali. from Ohio.
My shop will give boxes and packing to free to anyone who asks. We usually have some laying around, I'd definitely tip a six pack if they pull a new bike out of a box for you.
The most important things to get are the front fork brace and the r derailleur guard if you have gears. shift your derailleur into your biggest gear in the back it will help keep it safe, and don't forget to put your front QR in the box. I will usually put extra cardboard in the fork area to help against it poking/wearing through.
See if you LBS will actually ship it for you. We provide this at no cost if we package the bike. It costs less because UPS is there regularly anyway. If your shop will do so even though they gave you the box for free any didn't make anything packaging your precious cargo be sure to give them beer. On second thought give them beer anyways.
Insurance is cheap and recommended.
Good luck and enjoy your trip.