As others have said it really depends on the airline. However, I've flown internationally with IcelandAir and Virgin Atlantic with my bike packed in a Ground Effect Tardis bag and was not charged anything. It just went on as regular baggage, so it is possible to pack a regular bike into a soft sided case and either meet the size limits or exceed them by little enough to be charged nothing. Here's a video that shows how it works, but I use my gear as padding around the bike and make sure nothing can move around.
http://www.youtube.com/watch?v=raUiKoRu2Oc