I fly regularly and take my bike with me on flights at least 4 times per year it's no big deal. Some airlines include bicycles as part of your allowed baggage and others charge a separate fee. It also depends on your class of ticket whether there is a separate charge. At times it is worth the upgrade as the bike will be included for no additional charge. Can use old bike boxes from bike shops usually given for free or proper transport boxes which can be rented from bike shops or purchased.
Other lessons learned. Don't pack co2 cartridges as they will be confiscated. Remove Di2 batteries as this is becoming an issue and need to be placed in your carry on. Let the Airline know you are bringing a bicycle as sometimes they have a quota and bikes will be left behind. (Last year flying from Bordeaux a group of 30 showed up with bikes and approx. 10 were left behind. Mine made it because I booked ahead.) Let some air out of your tires as the Airlines seem to think that's important.
Have fun!