Depends on the train. The big cross country trains require that you box up your bicycle and charge extra to transport it. Some of the regional lines may allow unboxed bicycles at no extra charge. I believe the california coaster may allow bikes on.

I met a couple of guys out of Cincinnati that got around the extra bicycle charge by putting their bikes inside huge hockey gear bags, with the wheels removed of course. Amtrak was supposed to charge extra for oversized luggage too, but they let these guys on. I don't think you're going to be able to fit an extracycle in a bag though. And i wouldn't advise for anyone to try. I think one of the derailers was bent in the process of stuffing the bikes in the bags.