Yes tails bleed if you over pull, if you take your time then they don't bleed. Its because the skin on the doc is very very thin and easily broken. In the mane the skin is thicker and has far less nerves
I'm not suprised your horses don't like thier manes being pulled if you are causing bleeding. I still can't work out what you are doing to cause bleeding in the mane? Even when pulling great big chunks out of a cold horse I've never yet made one bleed.
Done properly there should not be any blood and the horse should not feel anything other than a little bit of pressure.