In my opinion, both Playboy Bruce and Batman are exaggerations of Bruce’s true self not masks necessarily. The real absolute Bruce is the one most don’t see, the one in the cave or that comes out when with his loved ones. Playboy Bruce is the egotistical and cocky self of Bruce personified and multiplied. While Batman is Bruce’s rage and pain personified and multiplied as well. They both are extensions of Bruce and represent parts of him but aren’t necessarily completely who he is.

I could not agree more. I was actually writing a lengthy reply about this when I saw your comment, which is so much more concise. I have a slightly different take on the playboy aspect of his personality (though I also agree with yours). Here's my lengthy ramblings about it.

I've always seen the one true identity as being that Bruce you see in the cave with Alfred or Dick. He's a very different person in those sorts of moments than when he dons the cowl or a fancy suit. Bruce is someone who has been stuck in a sort of state of arrested development, still dealing with the trauma of his parents deaths and the playboy Bruce Wayne and The Batman are both masks he wears to deal with his trauma and express different, repressed parts of himself.

The Batman is about his need for vengeance and justice, driven by his own trauma in order to strike fear into the hearts of criminals like the one that murdered his parents. This side also exists as a sort of wish-fulfillment, hoping to be that sort of hero who could have shown up to save his parents.

The playboy Bruce Wayne is also a sort of wish-fulfillment for Bruce. This one really depends on the writer because boy does this side of Bruce vary, but a portrait of the character's overall history paints a picture of a Bruce Wayne who isn't just a drunken playboy mask. It's a version of him seemingly less burdened by the trauma of his past and one who attempts to be connected to the world in which Bruce fundamentally isn't. It's who he could have been, had there been a Batman to save his parents, or who he still could be if he managed to finally escape that alley. It's also the part of Bruce hoping to live up to who his parents would've wanted him to be.