Hey! if you google it you'll find that the quickest, shortest route is to take 120 through Yosemite and BINGO! you're there, easy as ice.
A few years ago I met two Berkeley Ph.D's who both recently moved from the east coast, seemed to have a lot of mountaineering experience and wanted to do Whitney. It was, I think, January.
Since they impressed me so much and seemed to have it all together, I decided to just let them do it all and I would show up, hop in the car, relax and get to whitney.
Of course they googled the directions and when we got underway at about 8 p.m. I decided that these guys knew what they were doing––THEY were frickin' PH.D's at Berkeley . . . they had hairy scary stories of climbing on the east coast . . .
So naturally they knew something, some highway across the sierra that I didn't––one that was plowed, perhaps and very close to Yosemite . . . well, we got up there, into the valley and things started to fall apart and suddenly they realized their mistake and I . . . well, I finally spoke up. (no, we never made that trip)
ANYWAY, Yes, you have a long drive from gilroy to Lee Vining via bakersfield. Drive safely.