Can’t believe I just now saw your comment. You can get up to Sherman from Bakersfield. Take HWY 178 to Lake Isabella, then HWY 155 toward Wofford Heights, don’t take the left hand turn that 155 takes to go to Alta Sierra, instead continue straight on toward Kernville. That road will end after crossing the bridge over the Kern River, turn Left, and then keep going until you get to Sherman Pass road, it’s a sharp right-hand turn up the mountain.
Also, check out the Sherman Pass page here, it has the snow park marked on Google Maps, and you should be able to navigate your way up from Bakersfield.