The upper part leaving Yellowstone is on the north side of the valley, so an east bound passenger would have a good view of the valley below.
Here's a sample Google Maps Streetview (but with guardrails)
https://maps.google.com/?ll=44.470725,-110.062237&spn=0.030073,0.078192&t=h&z=14&layer=c&cbll=44.470814,-110.061952&panoid=CY-ZV1jO_7MQM4LCzIuKFA&cbp=12,90.49,,0,-0.1But if that's a problem, US12 just east of White Pass could be worse:
https://maps.google.com/?ll=46.656005,-121.337471&spn=0.014581,0.039096&t=p&z=15&layer=c&cbll=46.656003,-121.33759&panoid=ea3s9eUpEC24DjCd1Kx3vw&cbp=12,90.2,,0,-0.1In this Streetview construction crews are repairing a washout.
And then there's Going to the Sun in Glacier - which could be scary even in the tour bus.