There is a great FS campground called Robinson Creek up the road to Twin Lakes from Bridgeport. We've stayed there. Nice.
South of Bridgeport about 10 miles a road to the right takes you up to the Virginia Lakes, where there is a good FS campground called Trumbull Lake. Our favorite sites are closer to the lake. It's stunning.
Coming down into the Mono Lake Valley, there's a bunch of FS campgrounds as you head up to Tioga Pass from Lee Vining. The closest one to Lee Vining is Big Bend, which is NOT on the Tioga Pass road.
In the June Lake loop, there are several nice FS campgrounds - we prefer Silver Lake and Oh! Ridge, which is the closest to the 395.
While there are a few between June Lake and Mammoth, we haven't been to them. We don't use the ones in Mammoth, either, because of the crowds.
Convict Lake has a nice FS campground.
Then the Rock Creek drainage has a few that can handle big rigs, especially East Fork. That's our favorite. Rock Creek Lake CG's sites are too small - more for pop-ups and class B's. Along the 395 next to the turnoff for Rock Creek there's one called Tuff, but I don't know about the size of the sites.
About 5 miles W of Bishop is a campground called Pleasant Valley. While it's not FS (It's a county park) it's only $12 night. Might be $10. Definitely can handle big rigs. We like to go around and across the river and park right on the river.
Up the hill just before you drop down to Pleasant Valley is a BLM campground - usually used by the rock climbers in the Owens Valley Gorge. I don't recall seeing big rigs in it.
My blog:
Wanderlust '08 Keystone Sprinter 250RBS travel trailer
'10 Nissan Titan