Thanks Indyfabz, I hadn't thought about taking a train, do you have any idea how long it takes?
You don't have to take the train to ship your bike via train. Amtrak will ship your bike between certain places even if you are not a passenger.
But if you want to ride with your bike, it takes a while. If you leave Philly on a Monday you arrive in Seattle on a Thursday morning. It's a PITA these days since there is no longer direct service from Philly to Chicago, where you catch the Empire Builder to Seattle. You either have to go to Philly-Pittsburgh and change trains around midnight or go Philly-D.C. for the Capitol Limited or Cardinal to Chicago.
But if you have the time, the Empire Builder is a nice ride. I have done it twice. Highights include the Wisconsin Dells, the open plains of ND and MT, Marias Pass, where you skirt the edge of Glacier National Park and Stevens Pass in the Cascades, where you go through the longest railraod tunnel in the U.S. and span some very pretty gorges.