Well in general, most airlines will not carry Specialized bikes......LOL, only joking...
Genrally for domestic flights in the USA, it is around 70 USD per bike...... Each way..
Going International is generally speaking free, only time I had ever paid was in the USA, but it all changed a month ago. My main route is New Zealand to Europe, with a stop over in LA for work..... With some 19 baggage issues from 20 flights through London Heathrow, I started to only check my bags one flight leg at a time. So when I picked up my bags and bike in London to travel on to Barcelona, they now charge a flat rate for bikes and golf clubs of 150 Euro (250 USD) each way...... So keep away from Iberia Airlines like a bad sexual disease.....
British Airways, probly the WORST airline in the world are now not accepting surf boards at all, and I hear thoughts that they will also start charging for bikes....
I flew from Spain to London the other day on EasyJet, that was 50 Euro return for my bike, which was ok...
See the link attached....
http://www.setteusa.com/show.php/Accessories|Bags|travel_bag
I have had a great run with these bags, I can almost get 1 year out of one, keep in mind I am a travel whore..... They are a really reasonable price at PricePoint....
I have tried hard cases, far more hassle to break the bike down....
Using the Sette bag, I remove of course the wheels, handlebars from the stem and the rear der....... And the pedals of course......... The straps are what binds all together, the seat and the stem keep everything tight if that makes sense.... I do in the sleeves inside the bag on each side have a cardboard box flattened to give it support....
The worst I have had is a bent disk rotor, of which I now remove the disks.....
Hope that helps, the more stopovers with flight changes, the greater the risk is for damage and loss of bike..... So when you can fly direct somewhere, sweet as....