I recently used Amtrak to ship a bike across the country, with great results.
I used Amtrak because I was shipping a vintage bike (Raleigh) that I didn't want to disassemble enough to fit into the type of bike box that BikeFlights uses (think of the boxes you can get from your local bike shop). Amtrak's own box (about $15) only requires that you take off the pedals and turn the handlebars. The bike just rolls in, although I put a bunch of padding around the Raleigh.
Amtrak's price was about $80, which was much lower than $600 or so that FedEx or UPS would charge to ship such a large box. They'll take it from any Amtrak station to any Amtrak station. You have a few days at the end point to pick it up, then they charge you about $3 a day for storage.
If you can deal with removing the wheels, fenders, etc., to get the bike into a standard box, use BikeFlights. It's a little cheaper, and they'll deliver it right to your doorstep. If you don't want to take the bike apart, Amtrak is a great option.
--Eric N
Twitter: @CampyOnlyGuy