This is tricky, because Truman did, many times, reflect on his decision to drop atomic bombs. The problem is, he never made a decision to drop atomic bombs.

Let's back up. One thing that historians have known for decades, but has not penetrated into how people talk about the atomic bombs, is that they were not a product of a single decision (they were used as the result of years of "accumulated" decisions and assumptions, a process something referred to as institutional momentum), and that no "decision" as to whether to use them was sought or given by Truman. Truman was informed in an incomplete way about the plans to use the atomic bomb (he always referred to it in the singular, which is interesting and important, for reasons I'll touch on) while at the Potsdam Conference. It was never presented t him as a situation where he would have to make some choice; it was assumed that he was fine with all of it, and Truman's lack of intervention seems to have just reinforced that. (He could have said, "don't do this!" and it would have been respected to some degree. But he didn't.)

Truman himself only really participated in one "decision" before Hiroshima and that was in siding with the Secretary of War, Henry Stimson, about Hiroshima being the target of the atomic bomb, and not Kyoto. That is an entirely other discussion to have (my theory is that he got confused by that conversation and did not realize that Hiroshima was a city filled with civilians, as opposed to just a military base or outpost), but it's important to note the framing there: not whether the bomb gets used, but a decision between two different targets.

Other than that, Truman was kept pretty far out of the loop. He was enthusiastic about the atomic bomb, based on the account of the Trinity test he received, and because it seemed like it would give him leverage against the Japanese and the Soviet Union. Neither he nor anyone else seems to have thought that it would immediately end the war — they were caught quite off guard by how swift things moved after the bombings and the Soviet invasion of Manchuria. He also appears to have been totally unaware that two bombs would be dropped in such close succession (my point about the "singular" usage above), and that the launch order which he saw (but did not give) was really a blank check to the military to drop as many atomic bombs as they had available. So Truman was more out of the loop than he appears to have even realized, and after Nagasaki and the accounts of high civilian casualties made their way to his ears, he actually did take control of things for the first time and asserted (on August 10th) that no further atomic bombs could be used without his direct order. He told his cabinet that day that he had done this because he couldn't stand the thought of killing "all those kids."

So this is the sort of complex reality that gets poorly boiled down as "the decision to use the atomic bombs." The "decision" version of the story didn't really get formalized until 1947, after there had been mounting criticism of the atomic bombings as unnecessary (often from high-level military leaders who feared that the atomic bomb was taking away from the glory and future funding of the conventional military forces). Truman's former Secretary of War, Stimson, wrote a highly-influential article in Harper's Magazine on "The Decision to Use the Atomic Bomb" that essentially streamlined the actual complex history of it into a highly rational process, one that weighed carefully the civilian casualties against using the bombs versus the military casualties in an invasion. Which is to say, the "decision" narrative you are familiar with. And it put Truman in the role of chief decider.

Truman himself liked this version of the story, even if he was quite clearly conflicted about the atomic bombings. Truman's own internal moral/ethical standpoint was that even if he wasn't that directly involved in the bombings, he was ultimately where "the buck stops," and he always took all that was done as part of his responsibility. And so he adopted to the narrative of him being the actual "decider" quite well, as well as the moral evaluation it implied, even though he must have, at least in the beginning, known that it was false. (After anyone re-tells a story about themselves a thousand times over decades, it is probably harder to distinguish what really happened from that story; I suspect Truman's own memories of this stuff changed over time, which is in part why memoirs are such dodgy sources.)

So, anyway, to circle back again, Truman did write and talk about the "decision to use the bomb" quite a bit, including in his memoirs, which were published in the mid-1950s. His public statements and writings on the matter were almost always of a certain character: this was a hard decision to make, but ultimately it was the right decision, and he never had doubts about it. And the more that the atomic bombings were criticized, the more he doubled-down on them. So, no surprises there — this was his legacy.

What is more remarkable is that many of his private statements, as recorded by his contemporaries, were much more ambiguous, especially closer to the event in question. He really appears, throughout his life, to regard the atomic bomb as a sort of evil invention, a thing that exists primarily to slaughter innocents, and not a "military weapon." He appears to have developed a deep distrust of the military mindset and their judgment about such things, and throughout his presidency worked to keep atomic bombs essentially out of their hands (they were kept in civilian hands). He also codified the system that existed after August 10th, in that the president would be the only person who could decide whether atomic bombs would be used — again, with the contrast being between that and the previous system in which the military essentially made the decisions. And it is clear, from several interactions he had, that he found the bombing of Hiroshima and Nagasaki a rather sore topic, one that he had deep moral doubts about, and one that anguished him in some way when he truly admitted to it. What he absolutely would not countenance, though, was someone who he felt was not sufficiently involved questioning what happened, or taking a moral burden onto themselves that was larger than his. So he was vehement in defending the bombings against criticism, and he was also scornful of people (like J. Robert Oppenheimer) who thought they had more blood on their hands than he did. It's a complicated psychological situation — but not an incomprehensible one — to have deep doubts about something one did, but then to defend it against critique. Which is just to say, even in his own self-accounts, Truman is sometimes taken as a one-dimensional figure when it comes to the bombings, but the documentary record suggests something much more complicated.

The best overall book out there on Truman and the bombings is probably J. Samuel Walker's Prompt and Utter Destruction. On the "decision to use the bomb" myth and its development, Gar Alperovitz's, The decision to use the atomic bomb and the architecture of an American myth is, despite much of the book being pretty motivated towards one particular interpretation of the bombings, an excellent study of the development of the Stimson article and its consequences in its later chapters. On Truman's complex psychological responses over the years, Robert J. Lifton and Greg Mitchell's Hiroshima in America: A Half Century of Denial contains some amazing anecdotes and recollections from people near Truman (including an amazing "mock trial" for Truman's soul that Churchill subjected him to over dinner, which clearly disturbed Truman despite Churchill trying to encourage him that his actions were defensible). On Kyoto and Truman's later aversion towards atomic bombs, I have published an article on this, and I am expanding this approach and interpretation into a book in the near future.