I say two.
Bruce Wayne the billionaire playboy is a mask and doesn't deserve to be called a face or side because he's a complete lie and doesn't reflect any part of his true personality.
Bruce the Real One witnessed his parents murder thus has the compassion to be a father figure to his Robins (and their alter-egos of course), a philanthropist, and keep his family's business going.
Batman is his darker side who through Bruce has the pain and drive to do what Bruce can't do as an ordinary person. He serves as a hero to Gotham and a knight for justice.
The two latter are who he is just different sides that cannot exist without each other whilst the former is the only mask Bruce actually has, but is as important as the latter two because it keeps his identity safe.
Bruce Wayne the billionaire playboy is a mask and doesn't deserve to be called a face or side because he's a complete lie and doesn't reflect any part of his true personality.
Bruce the Real One witnessed his parents murder thus has the compassion to be a father figure to his Robins (and their alter-egos of course), a philanthropist, and keep his family's business going.
Batman is his darker side who through Bruce has the pain and drive to do what Bruce can't do as an ordinary person. He serves as a hero to Gotham and a knight for justice.
The two latter are who he is just different sides that cannot exist without each other whilst the former is the only mask Bruce actually has, but is as important as the latter two because it keeps his identity safe.