Living in Nashville my favorite train trip is a Southwest or American flight away. My favorite Amtrak train I ride two or three times a year is the full trip Chicago to Emeryville on the California Zephyr. Love the trip between Denver and Grand Junction the most but the Sierras Reno to Colfax is just a spectacular. Will be riding the CZ both directions in December just so I can ride in Car 532 and 632 while the sleepers are still on the rear end of the train.
Don't they have Thruway Buses that serve Nashville?
They do, but my impression is they are not 'dedicated' Thruway buses, but rather regular Greyhound runs that have through ticketing with Amtrak. If I am right, I would prefer to fly to my train versus a long Greyhound ride (and I speak from experience).
It's also a matter of timing.
8255: to CHI: 3:00AM-2:00PM (11 hours on a bus and a really early wake up call!)
8251: to IND: 2:20PM-9:10PM ET
8317: to IND: 7:00PM-2:00AM ET
8850: from CHI: 9:45am-8:45pm
8850: (same bus): from IND: 3:20pm-8:45pm
8250: from CHI: 3:25pm-2:00am
8250 (same bus): from IND: 8:50pm-2:00am
8856: from CHI: 11:05pm-10:45am
8856 (same bus): from IND: 4:25am-10:45am
So to get to the west coast/Texas, your best bet would be to take 8251 to IND, stay overnight there, and take HS/Cardinal (depending on day) to CHI. You could take 8255 to CHI and leave same day for the CONO or a night Hiawatha. Maybe you could make the SWC (3pm departure). Ideally there would be a train that would leave Nashville 10-11pm at night and arrive CHI early in the morning and you'd leave for the SWC/CZ the next day. The 8856 is a little late to wait for coming back from California (but I'm sure at times the SWC/CZ has arrived in CHI that late before). Ideally there would be a 7:05pm bus out of Union Station for Nashville. Then again, all of the buses shown serve Louisville and if it served Nashville conveniently it serves Louisville during the graveyard shift (of course 8255 does serve Nashville in the graveyard shift). Of course, Greyhound sets the bus schedules, not Amtrak.
As for going from Nashville east, 8251 does time fairly well with the eastbound 50 and avoids too bad hours. Unfortunately after getting back from 51 (5:15am, you're stuck at IND until 3:20pm. There, you probably hope it's delayed for a long time. If you're not afraid of flying, flying is the better option than a bus (then again if you're not afraid of flying why take a train cross country in the first place?)
8850: from CHI: 9:45am-8:45pm