I have had good luck with both FedX and UPS. Keep the box small enough and the price will probably between $40-$60. A bike shop will probably charge and additional $30-$60 if you ship to them and let them assemble it.

That said, my first choice is to fly with my bike checked as baggage. Southwest will charge you $50 and it will count as one of your checked bags (the other checked bag is free). Frontier is supposedly about the same deal, but I have not used them. I get a kick out of riding right out of the airport.