That video is really helpful. I've been looking at the Stanislaus Nat'l Forest map, so I was able to recognize a lot of the road numbers you called out.
Bower cave is right after the turn north on Buck Meadows Road, if you're heading east from Coulterville to the switchbacks above Briceburg. It isn't a deep cave system. It's akin to Masonic Caves in Volcanoville, where it's a large outcropping of limestone with some more or less open air chambers on the sides. It's on a short trail up from the road that starts near a stone monument. I passed by but didn't go up as I had heard there was a fence part way up and the cave was on private property.