A polar bear’s fur is not actually white, it is translucent. It only appears white because of the way it reflects incoming light.
You can see the translucent hair below.
The hair is translucent because it is hollow, allowing for pockets of air within the hair to hold on to heat for longer. In effect, evolution has provided polar bears with an arctic insulator.
Also, notice that polar bear skin is black, which absorbs the most wavelengths of light and therefore generates more heat. If you need help conceptualizing this, the absorption of more wavelengths of light is the reason why a black car will be much hotter than a white one when left in sun.