I get the impression if your bike is boxed and checked baggage (with all that entails), Amtrak will transfer it on and off their Thruway coaches. Folder? You're probably good. Otherwise?
I've searched the Amtrak website and can't find a written policy for bikes and various journey permutations of train→bus→train. Maybe I'm missing something. Anyone? Bueller? Bueller?
While writing your senator or emailing your favorite cycle advocacy organization, see if you can get a favorable written policy on Amtrak Thruway buses + bikes.
All my Amtrak experience is when boxed bikes was the only option.
When I did GAP and C&O in 2013, we boxed the bikes (that was the only option then) and at Chicago station Amtrak moved our bike boxes from the Empire Builder to whatever train we took to Pittsburgh for us. Same on the return, we bought boxes and boxed the bikes in DC for the return.
When I came home from Pacific Coast in 2014, we bought boxes and boxed the bikes in San Francisco for the California Zepher (spell?) and then since the train was late to Chicago, Amtrak put us up for the night and the next morning we had to find an Amtrak employee to find our bike boxes and bring them to us for the bus driver to load onto the bus. It was up to us to take our bike boxes out to the sidewalk for the bus. Bus was pretty full, the bus driver was not in a good mood when he saw the bike boxes that he had to load into the bus.
/For the start of that Pacific Coast trip, we rode Empire Builder to Portland and at Portland train station we had to haul our bike boxes out to the bus area. I do not recall if we put the bikes in luggage are or if the bus driver did. Bus area in the photo below. The bus took us to Astoria.
In Astoria the bus stop was just a sidewalk. We found a cardboard recycling bin at a pizza place a block from the bus stop to put our bike boxes into.