I just rode the Coast Starlight a couple weeks ago with a bike. You have to box it, but they have the boxes at the station. The boxes are supposed to be $15 but they usually have extra used ones that they will give you for free because people leave them at the station when they're done and Amtrak employees are nice and keep them. There's also like a $10 fee to check it.
To box it, you just have to remove the pedals and the handlebars, you don't even take the wheels off. The boxes are bigger than bike shipping boxes. You can literally ride up to the station, buy the box, and disassemble your bike in the lobby in like 5 minutes. Lots of people do bike+train tours and the Amtrak people are super good about handling bikes. You do need to have your own tools of course.
The only thing that sucks is that there's only one Coast Starlight per day and it's super duper slow.