When farming for fur, players must at least have two available inventory slots as the raw meat will be prioritized over the fur.
Keep a good distance. They have high health and high damage and they can outrun you without proper technique. Circling around a fire,then walking in a straight line when your warmth is all the way up, then circling around a fire again when you are cold. Repeat this process until you have killed the polar bear(s).
Spam clicking is a bad idea. Take time to run away from the polar bear, because when you swing a sword/spear, you slow down a little.
You can attack multiple at once, and even with a arctic fox or more.
The Polar Bear was added in the 'Winter Is Finally Here', along with meat and it's respective fur.