Before setting out on this search, I first looked at a compendium of James Bond lore entitled Amazing and Extraordinary Facts - James Bond by Michael Paterson, to confirm if such "existential" inner dialogue existed in the books.
. . . He was often exhausted, wounded or traumatized; he lacked humour, and occasionally even confidence. He felt periodic melancholy with his role and sometimes doubted whether the West had any right to feel morally superior to is communist enemy. He even, in one novel, 'shredded his nerves' with worry.
Interest piqued with the mention of "periodic melancholy with his role", and "sometimes doubted whether the West had any right to feel morally superior", I went to the complete library of Fleming's Bond stories.
After scanning the library, I can say that he did at times express doubts, and even regret, but mostly he tried to suppress these feelings as they would only interfere in the performance of his duties.
I will present the pertinent passages in the same order in which the books were published; however, the most telling information probably comes from Goldfinger (1959).
In the beginning of From Russia with Love (1957), Bond begins thinking over his youth, and the changes he has gone through.
what would that youth think of him, the secret agent, the older James Bond? Would he recognize himself beneath the surface of this man who was tarnished with years of treachery and ruthlessness...
Then, in Goldfinger (1959), it is mentioned several times that he does not actually enjoy killing, that it is his duty.
It was part of his profession to kill people. He had never liked doing it and when he had to kill he did it as well as he knew how and forgot about it. As a secret agent who held the rare double-O prefix - the licence to kill in the Secret Service - it was his duty to be as cool about death as a surgeon. If it happened, it happened. Regret was unprofessional - worse, it was death-watch beetle in the soul.
Later, he tries to rationalize his role as an assassin.
He was too tense, too introspective. What the hell was he doing, glooming about this Mexican, this capungo who had been sent to kill him? It had been kill or get killed. Anyway, people were killing other people all the time, all over the world. People were using their motor cars to kill with. They were carrying infectious diseases around, blowing microbes in other people's faces, leaving gasjets turned on in kitchens, pumping out carbon monoxide in closed garages. How many people, for instance, were involved in manufacturing H-bombs, from the miners who mined the uranium to the shareholders who owned the mining shares? Was there any person in the world who wasn't somehow, perhaps only statistically, involved in killing his neighbour?
But then he suppresses these feelings.
Bond's lips turned down. Cut it out. Stop being so damned morbid. All this is just reaction from a dirty assignment. You're stale, tired of having to be tough. You want a change. You've seen too much death.
In You Only Live Twice (1964), following the murder of his wife Tracy, Bond suffers a type of emotional breakdown. It is of a type that we would easily recognize today--a result of too much repression of emotions, and probably regrets over his life.
He felt like hell and knew that he also looked it. For months, without telling anyone, he had tramped Harley Street, Wigmore Street and Wimpole Street looking for any kind of doctor who would make him feel better. He had appealed to specialists, GPs, quacks - even to a hypnotist. He had told them, 'I feel like hell. I sleep badly. I eat practically nothing. I drink too much and my work has gone to blazes. I'm shot to pieces. Make me better.' And each man had taken his blood pressure, a specimen of his urine, listened to his heart and chest, asked him questions he had answered truthfully, and had told him there was nothing basically wrong with him.
In The Man with the Golden Gun (1965), it is mentioned twice that he does not enjoy killing:
It was all very fine to be told to “eliminate” the man, but James Bond had never liked killing in cold blood
and then again...
James Bond got into the car behind Scaramanga and wondered whether to shoot the man now, in the back of the head--the old Gestapo-K.G.B. point of puncture. A mixture of reasons prevented him--the itch of curiosity, an inbuilt dislike of cold murder, the feeling that this was not the predestined moment, the likelihood that he would have to murder the chauffeur also.
And then in the last story The Living Daylights (1965), Bond refrained from killing his target in an unusually merciful stay of a licensed execution. There is no adequate rationalization given: possibly he had finally found a way of reconciling his past with his future, or more likely, Fleming was looking to give more dimensionality to his most famous creation.