It's confusing, because people generally don't ride bulls. Where I'm from you gently back off from both bulls and bears.

I remember it as bears hibernate, so they will stockpile resources and not let go of them.

I don't really have an analog for the bulls, oddly.

Nice! I actually knew the correct term, though. Have a bad habit of switching binary things a lot. :(

Edit: Amusingly, I think I was thinking that I was bullish against it. Such that I flipped a different part of the sentence. Still, wrong as written.

Or: bears hibernate, bulls charge

I was taught it was how they attack.

Bears: stand and swipe down with their paw

Bulls: start with their head low and jut upwards with their horns