Characterization doesn't matter much in 2001. You can see this in part in the way the novel skips lightly from main protagonist to main protagonist: Moon-Watcher's the hero of the first part; Heywood Floyd of the second part; and David Bowman of the rest—which means you don't actually meet the ostensible main character until more than a third of the way through the book.
This switch from character to character might be jarring in another book. But in 2001 it hardly matters, because none of the characters have a personality to speak of. This is certainly true of Bowman, whose main trait seems to be that he is careful to not have any traits. There are several points in the book where he seems like he's going to have an emotion, or a reaction, and he pulls back instantly into bland, spaceman competence.
After Hal kills everyone on the ship, Bowman is at first sort of moderately upset ("I suppose you're pretty broken up about it" Hal comments (26.7)) but then he just goes back to doing his job, like he's the automaton rather than the ship's captain: "Work is the best remedy for any shock, and Bowman now had work enough for all his lost crewmates," (31.1) is all the explanation the novel gives us for how Bowman is able to shrug off the death of his friend and his own forthcoming demise. Later, when Bowman has been zipped miraculously across the galaxy, only to discover the alien race he hoped to meet is (he thinks) dead, he barely blinks:
Well, it was unreasonable to expect more. Already he had seen wonders for which many men would have sacrificed their lives. (42.22-23)
This goes beyond level-headed and towards catatonic. Bowman is a tranquilized nonentity. He is calm, not because he is a person whose psychology is calm, but because he has no psychology, and isn't really a fully fleshed out character. He's just a way to watch the exciting space events unfold. It's like every time Bowman might react, Clarke reaches down out of space and taps him on the shoulder to remind him that nobody cares about his reactions. "Just watch the double-sun, buddy," Clarke seems to be telling him. "Save the emoting for some other book."
Part of the reason Bowman is so bland is because he doesn't matter. But part of the reason is that he's supposed to matter transcendentally. He's not one person because he's the whole human race. In this sense, he and Moon-Watcher and Floyd are all one. They're all part of the great progress from the earth to the moon to the solar system to the stars.
You can see this most clearly at the very end of the novel, when the aliens are messing with Bowman's brain and rewinding his experiences. You zip back through the book, there's Saturn, there's the last talk with Hal, there's poor murdered Frank Poole. And then you go further back…but you still don't find out anything specific about Bowman. It's all generic; he could be anybody:
Faster, faster he moved back into forgotten years, and into a simpler world. Faces he had once loved, and had thought lost beyond recall, smiled at him sweetly. (45.9)
Who are those faces? Well, you can fill in the blank. They're faces you know, or they might as well be. Bowman has no particular experiences to get in the way. He's a more boring you.
This means that at the end, when Bowman turns into a space baby, you could be turning into that space baby too. The New Age, quasi-religious future faith in evolutionary apotheosis is for everybody. It is not just Bowman, but the human race, that is destined for great things. It is not just Bowman who will become an awesome energy critter—you will too.
Bowman is not really meant to be a person with feelings and emotions and character development. He doesn't undergo internal development and learn stuff, because if he did that it would distract from the magic transformation into the space baby. You can't be a human being and a space baby both, and the novel, by far, prefers space babies.