Flying to Europe? There are plenty of European air lines that don't charge for bikes, don't require they be boxed or crated and treat flyers like customers instead of criminals.
The only one that has a 'free' policy is Virgin Atlantic where they are carried as sports equipement
British Airways do too, but you must get under a certain size and weight (23kg) not impossible
Icelandic air are opening up a few routes, but do charge
I flew United 2 years ago as led a tour round Yellowstone and they were the only connecting to Jackson from the UK. $150 dollars each way