Also, I checked out SWA's policy. Looks good as long as you have a good box:
Non-motorized Bicycles, including Bike Friday and Co-Pilot, will be accepted in substitution of a free piece of checked baggage at no additional charge provided the bicycle is properly packaged and the box containing the bicycle fits within the 62-inch sizing limit and weighs 50 lbs or less . (Maximum weight is 50 pounds and maximum size is 62 inches (length + width + height) per checked piece of luggage). The handlebars, kickstand, and pedals must be removed and placed inside the box. A $50.00 each-way charge applies to bicycles that don’t meet the above criteria. Bicycles packaged in a cardboard box or soft-sided case will be transported as a conditionally accepted item.