He is an actor, but not a big, big, actor like many others. He is actually more famous in Japan than he is in his own country, because he has gotten older, and the parts pass him by. The lounge singer would never make it in America, or if she and her band did, it would be in small, insignificant clubs. She represents what Bob's career could turn into - second rate and forgotten, and so, she is somewhat like another form of reality and conscience for Bob. He knows it would be very easy to become just what she is. There are many things that keep Charlotte and Bill from connecting. Their ages are quite different, and that is a barrier, although they do work through that somewhat. They are not really communicators, and so, when it comes right down to it, their language, their communication, and their understanding of each other is all undeveloped at best. They are two lost people trying to connect it a distinctly difficult world, and that is really all they have in common. They do not connect, really, because they do not understand themselves, and so, they cannot understand each other, the real world, or even the make believe world they inhabit as they explore Tokyo together.

At first, I thought he whispered that they would see each other again, and they would end up together, but clearly that was not so. Perhaps he told her that he loved her, but that would not make both of them smile, it probably would make both of them...

Bob has a wry sense of humor throughout the film, so perhaps he cracked a joke about their time together. It would not have been a deep thought, because neither of them really communicated deeply during the film. On the other hand, he simply could have told her that he had the time of his life, and would never forget her. I like to think that is what he said, but the whole idea is that we will never know, and we make up our own ending.
This film is not about real life, and yet that is what it is ultimately about. Both Charlotte and Bob must return to their real lives, and leave the unreal life in Tokyo behind. Their relationship would not have happened in America, because they never would have been drawn together in the first place. In Tokyo, they were alike, in America, they were not. Therefore, the film really makes the viewer think about what is "real" about life, and how to alter that reality. It is clear both Charlotte and Bob are not the same as they were when they came to Tokyo. They have new experiences, new ideas, and even, new realities that are available to them. They do not have to stay in their unfulfilling relationships, they have other choices, and they already began making them in Tokyo. Therefore, the film is really about reality, and how we all, no matter who we are, can change our realities if we only want to badly enough.