I most loved how Kevin Conroy's Batman from the Animated Series portrayed this aspect of the character. Conroy did measurably different voices for Batman and Bruce which made it completely clear that Bruce was the false persona being put on for appearances while Batman was the real voice and personality, and also sold how good Batman was at pretending to be Bruce when needed. Conroy's Batman isn't just a ninja genius detective, he's also a good actor, and to portray that as well as he did Conroy had to be an awesome actor.