So you are saying that you will be crossing Tioga Pass in early June -
Then heading across Nevada - most likely on US 6, eh?
Here was my route - at Crazyguyhttp://www.crazyguyonabike.com/doc/page/?o=1r4vFZo&page_id=26313&v=RE
(I took the route via Rachel and Caliente from Warm Springs.)
Notice that I had to take the long way around -
Because Tioga Pass often is closed until mid June.
BTW - coming into Yosemite from the West -
Hwy 140 is WAY, WAY better than Hwy 120.
Hwy 120 east of Yosemite and US 6 in Nevada are really nice.
They are even more remote than US 50.
You can get a minimum of food & water at Benton.
Tonopah has most services.
Then there is no developed areas until Ely.
You can usually beg water at the closed motel at Montgomery Pass.
There is a rest area with water 7 miles west of Tonopah.
There is a rest area without water 30 miles east of Tonopah.
(If you hand out long enough you can beg water from someone pulling in.)
Warm Springs is an abandoned bar/pool. Begging of water possible.
The Blue Jay Highway Maintenance Station - 15 miles east of WSarm Springs has water.
There's a funky, tiny store - the man is a tough sister - at Lockes.
Bar/cafe at Currant - sometimes there is someone home in the trailer behind it for H2O.
Lund is well off the route - but does have a little store.
I rec staying in old downtown Ely at the Hotel Nevada rather than out on the strip.
Course, you can always camp in the national forest above town and ride in the next a.m.