Somehow, a combination of this video and an adorable gif of a little girl learning to hop her balance bike made the light go on: "Oh! It's like an ollie! Jump straight up, then hop the bike!"
I was on my lunch ride last week, feeling pretty good about neatly hopping a curb when I realized my saddle was gone. It's clearly been broken for a while, and I guess the bouncing finally shook it loose.
Given how long it took to finally come apart, I can't bring myself to eat the price of a new one right away. I stuck it back on, and it felt exactly the same as I'm used to, so I'm just going to wedge it back in place and ride on for a while.