A lot of that specialness came from the crew involved. Cowboy Bebop’s director, Shinichirō Watanabe, delegated work. He gave the staffers at the Sunrise studio enough room to put themselves into the show. “As a director, there are times when I don’t feel like dealing with details,” he said.1
Source: How They Designed the Characters of ‘Cowboy Bebop’
Each person in the team is a master of their own craft and they were given the freedom to put themselves into the characters they created.