Amtrak's bike pages -
https://www.amtrak.com/bring-your-bicycle-onboard The FAQs page -
https://www.amtrak.com/onboard/bring...oard/bike-faqs tell us the Coast Starlight (the longest direct distance) has checked service.
In October 2023, I returned from Seattle to Austin via train. At that time, I took the Empire Builder from Seattle to Chicago and Texas Eagle from Chicago to Austin. I chose that routing rather than via LA in part because I had a roll-on service to bring my bike. This year am thinking of a ride from Portland OR to Reno NV and have made train reservations from Austin to Portland and a different set from Reno to Denver. So trains work for me and why I suggest them.