Question: In my story, I want a creature to be immune to bullets, but giving it bulletproof skin seems too obvious. I want it so that you could shoot the creature a few times at its seemingly vital spots (the head, heart, etc.), but it won't die right away and can still escape or attack you. The best way to make sure it dies quickly is by draining most of its blood, which means you have to get close enough to cause a large wound with a bladed weapon.

Yes, I know you can just use a really big gun or explosives to achieve the same effect, but in this scenario, the options are limited to something relatively cheap, lightweight, and doesn't cause a lot of collateral damage. To give you some image, the creature is about as agile, as strong, and as big as a polar bear.

Preferably the reason it's immune to bullets is based on real animals, or at least something that could exist in the natural world.

Answer: 
Um why not use an actual polar bear? Or something very similar; bears, especially the big bears, (Polar and Grisly) are notoriously hard to kill with small calibre rounds, the combination of muscle layers, fat, and fur over their primary body cavity makes getting at their organs really unlikely with handgun rounds. They also have very thick muscles and bones in their skulls so headshots often lodge near the surface breaking bone but not punching through.
Your creatures may have a reasonably thick layer of [ballistic gel](https://en.wikipedia.org/wiki/Ballistic_gelatin) or blubber-like material under their skin, which scope shall be to slow down and thus absorb most of the kinetic energy of bullets, sparing damages to vital organs.

You can either change the density of the material (shortcoming: it makes the thing heavier) or its viscosity to improve the effectiveness of the dissipation.