Southwest air and Frontier are the cheapest to fly with the bike. You'll have to box it up, but you can get a cardboard box from a bike shop, or maybe borrow or rent a case.
You can also UPS or FedEx it. This might be cheaper if you have a bike shop box & send it than if you do it yourself. Also requires a box.
Greyhound... nope, I wouldn't do that, not matter how cheap it was. I rode the dog half way across the country with my bike once - never again.