Hi Monica,
I live in Germany and have taken my bike on planes a number of times - this Saturday I fly Air Berlin from Hamburg to Fort Myers, Florida - going to connect with the Southern Tier and ride westbound -YIPPEE!!
I would never ever tour without my own bike that fits well and has been set up by me to meet my personal demands. Spare parts should not be a concern in the USA.
The only time I had a little damage (to a shifter lever) in transport was when I did a lousy, hasty job of packing it up coming home.
Before I leave, I take my bike for an inspection and ask them to save as large a box as possible for me for when I come back to pick it up. They usually give me a box that is so big that I just have to take off the front wheel, wrap it in bubble foil, put the seat down, turn the handlebars longwise, remove the pedals and let some air out of the tires. They give me a plastic spacer to fit into the fork for protection. I then put all of my gear including the panniers, helmet, clothing, tent, sleeping bag, etc. in the empty spaces in the carton. I take a roll of tape along in case they ask me to open the box for inspection.
Upon returning I have always gotten a box from a local bike shop - called before going there or asked ahead of time - and only once I had to pay for the box (in Spain).
Most airlines have charged me around US$100 one way to ship the bike to or from the USA, except the german companies, Air Berlin and Condor.
They charge 25 Euros one way and don't specify the size of the box, just a 30 KG weight limit. That is no problem for me, since my entire rig fully loaded (including the box)weighs less than that - I always try to go light. Of course, you have luggage allowance and can check in a piece of luggage (some old bag or garbage sack) that you can throw away upon arrival).
Air Berlin flies (at least in the summer) to San Francisco twice weekly for around 350€ from several german cities - their website is also in English if you want to check.
Good luck and have a great time!! Susan