FPS is not the genre for blood/gore, you'l be wanting a hack n' slasher along the lines of Ninja Gaiden or Lolipop Chainsaw or something. Alright so Dead Space has a fair bit of blood and could be called an FPS, and Spec Ops: The Line is just a massive depression-fest....you could give those a shot.
The original Crysis had almost zero blood, C2 had a bit with all the people laying around rotting/dying, the most blood you'll see in Crysis 3 is when you do the stealth take-downs...and even then it's only enough to fill half a glass (half full, yeah!) or so. If you want bucketloads then hack n' slasher is the way to go.
Bullets aren't known to cause a huge amount of bleeding anyway, a target exploding in blood after being shot would make no sense unless Crytek felt like being silly. Not unless Marshall had the ability to blow limbs off and Typhoon could make everyone in the area instantly die out of fear of getting impaled by 5 billion bullets.