Why isn't liver bitter?
A few items that when added up result is a lack of bitterness:


Though bile is produced in the liver, it ends up being stored in the gall bladder for both humans and cows. I wouldn't expect the liver to be full of bile as a result.
One of the main functions of the gall bladder is to concentrate the bile by removing water and electrolytes from and making it, presumably, more bitter in the process. This also makes liver bile more soluble and thus can dissolve into water or other common cooking liquids more easily.
Typical butchering of the liver removes most of the hepatic duct, which is where a lot of the bile in the liver would be.