I fly with bikes a LOT. Beaters taken one-way to Mexico and points south, custom S&S coupled bikes, a Swift folder. It doesn't matter who you talk to on the phone. The only person that matters is the smiling, or scowling, underpaid person at the check-in counter. Well in advance, get a box or two from the LBS. Get some extra cardboard. Take your bike apart as far as you are confident doing. If you can take it down to a frame, with wheels off, left side crank off, rear deraileur disconnected and taped to a chainstay, bars and stem off, etc.; fit it in a box the size of a BMX bike box. Reinforce the box with an extra layer on the sides and some rolled cardboard cross pieces. Try for a packing system that will allow the TSA inspectors to easily pull the whole thing out as a unit, look at it and slide it back into the box. So, don't tape the top of the box shut, make sure it is obvious how to open the box for inspection. Smile, be nice, and the airline may take it without charge. My point is... make the box as small as you can, Do everything you can to make inspection easy, corral all the cables and parts in the box, tape it all together. At check-in be positive; be pleasant about the process. It is their call, but I have had good luck for going on six years. I have yet to pay an up-charge for any bike. Good luck. It's easy to talk yourself out of it, but it’s always worth taking your bike.