Bob's Conway summit idea got me to thinking...

Sonora Pass (Hwy 108) is a little closer. PCT trail head is at the pass, and there's a wide spot half a mile west of the pass where I have bivied overnight before. It's 15 miles (30 minutes) off the 395. You will wake up to some beautiful scenery.

Looking at Google Maps in the Hwy 88/89 area, there is a loop off the 395, and maybe Leviathan Lookout Rd (elev 8400 - 8800) might work (but I have no idea how good/bad the spur off the main road is)

I think no matter where you go, as Bob says, you can probably bivy by your car. Whenever I do that, I get there after dark, and get up at dawn. Except for heavily traveled roads (and they're too noisy to sleep), nobody would even find you.