I have made this trip several times and find the best way from the GC is back on 89N to Page, Zion, Bryce, then west on 20 to I-15N, to SLC,on to Logan on 89 right to Jackson...go North to The Grand Tetons and on to Yellowstone.
However Fishing Bridge is way out of the way and I prefer to dry camp or partial hook-ups in several NFS campgrounds in W Yellowstone. Grizzly is without one of the best campgrounds you will ever stay in but pricey.
jdarling10