I recently flew on American Airlines from Dallas to Boston and back with two folding bikes packed in Samsonite hard sided suitcases. The suitcases are the largest size they make that are under the airline size limit and the folding bikes just fit with a bit of creative packing. I was not charged any extra fees either direction.
TSA opened both cases for inspection on the way up but not on the way back. Everything arrived fine each way. This, I believe is the best way to go if possible. Because you have a normal suitcase, there is no question about extra charges. The weight was 10 lbs below the 50 lb overweight limit so there was no problem there either. Of course, you have to find a place to store the suitcases, but in our case we were staying in a hotel and touring from a stable base so it was no problem.