Greentext

I think the penguins would learn to just swim away, and the bears would starve since they would need to expend a lot of effort for a small bird versus the calorie-dense seals they're used to.

This reminds me of a friend that once proposed that if we really wanted to mess with Europe we could release a few packs of coyotes

I was really hoping OP wanted to drop the polar bears on a tropical island. For science.

Etymologists crying and shaking right now at the thought of Antarctica (meaning: without bears) gaining the one animal it's not supposed to have

Antarctica is generally colder than the Arctic. They would almost certainly be stuck along the coastlines of Antarctica like the penguins are, since the interior average temperatures rival the coldest ones ever recorded in the Arctic. They should be fine there, but then that means they have a very limited distribution and that penguins and seals consequently are always forced to share an environment with the polar bears. Because they're not used to the polar bears, their populations would likely be destroyed, leaving the polar bears to starve. Unlike in the Arctic, too, they would have nowhere to retreat if their food supply ran out. Outward is hundreds of kilometers of ocean, and inward is hundreds of kilometers of unsurvivable desert.

I've recently learned that bears absolutely love cocaine. I'm sure that's relevant here somehow.

You may find you struggle with step 1.

Would work until the penguin pop. is too small and then they start dying out again

I'd say that if all you want to do is scare the shit out of some scientists in Antarctica you probably only need 1 polar bear

would have to be quite a few bears to avoid heavy inbreeding

Sounds reasonable.