Anytime I have ever travelled with a bike, on a plane or greyhound, I put the bike in a hockey bag. Although I did this with a BMX bike, I think you could do the same with a full size bike. You could use all of the gear/clothes for padding for the bike. I guess the only risk is if they toss the bag around like hockey gear.
And I usually make cardboard walls surrounding the bike, and bubble wrap/cardboard throughout to keep it sturdy and the parts in place/protected. I have never been charged anything extra for this on planes or greyhound.