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.
**FUR**

What about a massive stubborn fur, that is thick enough to absorb most of a bullets energy or/and deflect it from it's original path.

**HORNS**

The creature also could have horn like growths around its vital spots, which can deflect a bullet from the vital area when incoming on certain angels.

This still mean that a bullet may be deflected to a less vital area or if shot at the right angel (which might be difficult) still might hit a vital area. This makes it also very challenging to hunt such a creature.