Yes, the next road pass north of Tehachapi is Tioga in Yosemite NP. Did Google really route that way over the trails? Even if it's not wilderness (no bikes allowed), you really don't want to go that route!

You may just want to go south and around the bottom of Death Valley. It's extremely low, but flanked by high mountain ranges. (off topic) Geologist now think that from 90 MY ago to maybe 12 MY ago, the area east of the Sierra was a high plateau, like Tibet or the altiplano, and the Sierra was just the shoulder of this plateau, so have been uplands for a long, long, time. Since 12MY ago, the underlying hot subducted slab has vanished, letting the "nevadaplano" succumb to crustal extension and collapse, even to far below sea level if you look at the bedrock floor under Death Valley...