Interesting, I saw no bears when I did this in reverse years ago, altho they’re around in spades for sure. I DID see several rattlesnakes around Pate Valley, which is notorious for them. For me, much worse than bears.
I climbed up to White Wolf from around Pate; either way, going up or coming down, that section of trail is a steep route for sure, and pretty long.
I did this in the spring when I discovered the route I wanted to take was completely snowed in. So I went down instead, though the Grand Canyon. Of course the issue then is having the Tuolumne cover sections of trail that run at the base of cliffs. I did manage it on a pretty big snow year to boot. This is a decent spring shake down hike.