FYI, I recently shipped a bike via Amtrak with great results. Amtrak sells their own bike box for about $15, and because it’s oversized all that’s necessary is to take off the pedals and turn the handlebars. The bike then just rolls in (I added foam padding when I shipped the bike), which makes it much easier to pack.
I shipped a bike this way from California to Syracuse, NY, for $84 including insurance, and it arrived in about three days. Amtrak will ship to any of their stations and then hold it there free for several days and $3 per day thereafter.
If you have the time and are OK with disassembling the bike, BikeFlights or other similar options is a great choice. For those of us who have bikes with racks, fenders, etc., that are a little more difficult to take apart, Amtrak is worth looking into.