I have taken my bike from Denver to Emeryville by Amtrack. They provide a box for $5 and a baggage handling fee of $10. Never any problems. I am going to Italy this summer and purchased a Ritchey Breakaway with Case. Should be easy to pack so TSA can inspect and repack. I am going to remove the tires and tubes and fold them with rubber bands so they can easily inspect everything without taking too much out of the bag. I may or may not be charged for oversized baggage. I will try and pass for AL legal.
If you plan on travelling often with a bike then get couplers and a case.
Build a bike box like a gift box and use straps to hold the box together. That way they will lay the box flat, remove the straps, and open the box so that the entire bike is exposed. That way they won't have to remove and repack the bike in the box with much effort. Just an Idea.