Does that solve the problem?
To me - it does not. In US outside of Manhattan if you do not have car, you are without legs.
Look, you have to rely entirely of bus schedule and itin they create - you are not going to have any leeway outside of bus stops at scheduled places. If that works for you - go ahead, but just remember - Yellowstone is three times larger than Singapore, you can't and won't be able to see it in two days or two weeks even when have your own car.
P.S. Checked the link - it says Yellowstone AND Mt Rushmore. AND the start City is San Francisco:
Take a look at the map - it is 1500 miles distance.
I've driven from San Francisco to Yellowstone, it required stop at Twin Falls for night and our average drive speed was 80mph. Bus will go way slower.
Translation - from 6 days you 3.5 day will spend on road. They will bring you at Yellowstone, take to Old Faithful, give you two hours to take photos and hush to another place. You won't see anything.
Take my advice - get someone who drives and get a car.
