I have used Amtrak many times as part of a bike tour.
On my summer tour thru 11 western states in 2019, I used Amtrak twice.
Once towards the end - skipping eastern Washington when it was almost 110 degrees.
Then at the end of the trip from Albany, Oregon to the Bay area.
FYI - Many train schedules have been reduced to every other day because of Covid-19.
So it makes it even harder and you have to plan even more carefully.
There are basically two types of Amtrak trains.
1) Long-distance, overnight trains - Most have baggage cars which accept bikes in boxes.
Recently, nearly all now accept unboxed bikes stripped of all pannier, etc.
The problem - this service only is possible at stations with baggage service - which are limited.
2) Short-distance day trains - Many, but not all, accept a limited number of roll-on bikes.
Again, you have to strip the bike of any panniers, etc.
The long-distance routes are usually one train per day. (Every other day now)
And the times of arrival or departure can be ugly - for ex. 4:15 a.m.
Not to mention that long-distance Amtrak trains are almost always late.
(Except when you are late getting to the station - then they are on time.)
It takes some planning, but once you know how to do it, it really is easy.
Amtrak has a very generous baggage allowance - so you can just load up and relax.
Also, they have always treated my bike well in baggage.
Except for the one time they left one station too soon (75 miles away) - which delayed me a day.
Only really big mess-up in 30 years.
And it's usually way cheaper than flying when you add the airline baggage fees.
Don't even think about Greyhound unless you enjoy torture.