Has anyone done this before?

I would like to ship my bike and ride a train to the west coast this summer. It would take only two or two and one half days to get there. We could see the scenery during the day and sleep at night while the train was still heading us to our destination. Once there, we could flower sniff our way back home on the bikes. Sounds like it could be some fun.

Anybody done this or have any suggestions? Amtrak will send people, but I don't know about the bikes.

Thanks, Terry