Well now AA charge for all checked bags on domestic flight, unless you are Exec Platinum, platinum etc. Reading the new rules, it seems like most bike boxes, over 62-dimensional/linera inches should pay $100 + checked bag fee. So if you check a bag, and check a bike box, thats $125 for the bike.
For International flights, baggage is governed by the 1929 Warsaw Convention and later amended by the Montreal act, along with the airlines liability. So all airlines traveling International at least between Europe and the US have the same rules. You get 2-pieces of checked luggage included. The new rules say that you have to pay the $100 each way, unless under the 62-inches and 50lbs.
I called AA this afternoon and had a long discussion with an agent in their specialist luggage team. She confirmed the above for normal customers. She also confirmed that bikes are excluded from the $100 fee if under 62-inches and 50lbs on domestic and international.
My advice remains as it always was. Don't overload your bike box. The agents who handle check-in always weigh bags for weight distribution on the plane. However, you'll rarely find one who has a tape measure or understands the rules. The specialist I spoke with didn't and put me on hold for quite a while when challenged.