Yes, John -
You have the general route.
Map -
https://www.nps.gov/yell/planyourvisit/upload/YELL_Tear-Off_Map2016.pdfThe South Entrance Road up to West Thumb is steep with no shoulder and drop-offs.
Also, it can be very hot.
The best time to ride it is early evening when the traffic dies down and the pines provide shade.
(In July in Yellowstone, the sun does nt set until 9p and twilight lasts another 45 minutes.)
Even though Lewis Lake has mosquitos, I prefer it over the massive number of people at Grant Village.
A super early start the next morning allows you to explore the empty geyser walk at West Thumb.
Then it is still early for the road - with shoulders - along Yellowstone Lake to the Lake Hotel.
BTW - There is an almost totally empty old road to Gull Point where you can absorb the lake views.
The causeway on this old road is another peceful, empty spot.
After Bridge Bay - another massive campground with no privacy -
The is a unmarked bike trail that leads to the Lake Hotel and Lake Village.
The views here are spectacular - and the hotle is my favorite in the park.
I love having breakfast, lunch (usually) or dinner in the glorious dining room.
There's a little camp store as well for essential supplies.
The lakefront here is one of the most splendid vistas in the world.
Next up is the ride along the Yellowstone River and thru Hayden Valley.
I would wait until laer in the day, if possible, since traffic can be bad and the road is narrow.
I would use midday to explore the Fishing Bridge area - the museum and lakeside trails.
The Upper Yellowstone River is one of the Blue Ribbon rivers of the West.
Even if you don't fish - take time to turn off and enjoy.
Then comes Hayden Valley where you will sees herds of Buffalo - at a distance, please.
Cars have to use pull-outs, but you can find a hilltop away from the crowds.
If you are only staying one night at Canyon, then do take South Canyon Drive.
The view of the falls from Artist Point is busy, but worth it.
No one takes the trail that heads along the canyon's edge - but there are no rails, either.
(If you are staying two nights, I'd come back the next day.)
North Canyon Drive is another zoo and is an indictment of the park service and the American public.
It should be closed to all private motor vehicles and open only to shuttles, bicycles, and pedestrians.
But such is not the case. And you have to deall with the crowds to see the views.
Also, N. Canyon Dr. is the easiest way into Canyon Campground.
Canyon Campground is large, but most hiker/biker sites are off by themselves.
Be bear aware. Never eat in your tent, don't use a tent you've eaten in.
Store all your food propery and sleep in clothes that haven't been around food.
>>> You'll be fine - don't worry.
Canyon has all services and excellent ranger programs.
It's really worth two nights and magnificent hikes all day.
The Canyon-Norris Rd. is meh - just a connector with small shoulders.
A bit of a climb up and then a huge downhill - 45 mph - to Norris.
There are beautiful hiker/biker campsites at Norris.
Even if full, there should be a "No Turn Away" policy.
Norris Geyser Basin can also be very busy in the middle of the day.
There are so many trails and boardwalks that you have space even at noon.
But an early morning or evening hike is surreal.
(I much prefer Norris to Old Faithful.)
The Norris-Madison Rd has been recently rebuilt with small shoulders.
It's an easy ride along the Gibbon River past Gibbon Falls to Madison.
Madison Campground has a long tradition of ACA cyclists.
You are almost guaranteed to have cyclist company - maybe connect up for a few days?
Madison also makes a good base for a lightweight run to Old Faithful.
If you do - take the old road up the Firehole River - early if possible.
I would take Fountain Flat Drive and the trail up hill -
Make sure to climb the hill by Grabd Prismatic Spring to get the full colors.
There's a bike trail into Old Faithful - Warning! Insane crowds.
Then on the way back, take the quiet Firehold Lake Dr.
The West Entrance Road is scenic, with shoulders, and very busy.
(The is a short stretch of quiet, old road along the river.)
West Yellowstone is a zoo where you can buy little wooden bears made in China.
<<<>>>
This is all from memory.
I am fortunate enought to have ridden the park for 30+ years.
Including spring rides when the roads have just been plowed, but are closed to cars.
How lucky is that?