Ain't **** in southwest Kansas. I lived out there for a while. NM and Colorado are pretty though, probably plenty to see there.
I've taken the Amtrak to NM before. Technically it's not a route that they specify you can bring bikes on but they had plenty of room in the luggage car and I bet if you brought it in one of those fancy bike bags that some people use to get around baggage limits on airlines they probably wouldn't say a thing. Especially if you're a good tipper.