I've biked from the Bay Area to the North Rim a few times -
then on to New Mexico and points north.
For me is was usually about 20 days to the North Rim.
(I had a friend who worked at Phantom Ranch and I would hike down.)
Here a journal from 2005:
https://www.crazyguyonabike.com/doc/?o=1mr&doc_id=1168&v=sM#26316Most of the time I started between May 15 and May 23.
Tioga Pass was only open once - Sonora Pass is a bitch.
Further south that puts you at Walker Pass east of Bakersfield.
Further north you can take Carson Pass on the ACA Western Express route.
There are some very nice routes in the Coast Range if you are heading south.
Word of warning - Death Valley can be super hot by May - average high 100F.
That's the challenge of E-to-W in May in Calif/Nevada -
Still piles of snow in the Sierras and blistering in Death Valley.
There are not many good options across southern Nevada if you do Death Valley.
Because of the giant Nellis Air Force Range, you either have to go north to Tonopah or south to Vegas.
The problem with Vegas is massive traffic and long stretches of riding on I-15.
The problem east of Tonopah is extreme remoteness and lack of services.
In Utah you can either go via Cedar City and over to Kanab - big climb, less traffic.
Or via St. George to Zion NP to Kanab - Zion is spectacular in May, but more traffic.
<<<>>>
You seem to have more than enough time set aside for the whole trip - maybe a little more getting to G.C.?
Tioga Pass and Sonora Pass opening dates will depend on how snowy this coming winter is - looks meager now.
There are multiple ways to cross the Sierras then head east from Mono Lake to Tonopah.
The more northerly option is a chunk shorter - but you have plenty of time to do a longer southern option.
Have fun!