In his book, he shares painful illustrations of his mother's illness and is candid about his reactions to it. "I resented her for not being a mother. I didn't just resent her, I hated her for it," he writes.
Alda said it's important for families to admit these feelings, no matter how uncomfortable.
"You can hate people you love. I mean, it goes on all the time," he said. And he said he writes that he hated his mother, because "I felt I didn't have a mother."
Despite the grief it caused, his mother's mental illness was something that the family never discussed. "In those days, you didn't even talk about it. It was a shame, a dishonor to the family to have any kind of mental illness in the family," he said.
But through these difficult experiences, the young Alda developed a skill that would soon become central to his career.
"In order to survive, I had to watch very carefully what was happening. What was that look in her eye? Was she telling me about something that was really taking place, or was this a psychotic fantasy," he told Bashir.
As painful as it was, Alda said it made him a keen observer. "It made me super aware of what was going on around me, and I think eventually that was helpful to me as an actor and as a writer, because even when I'm on the stage, I'm focused on the other person," he said.
But getting work as a young actor was tough for Alda. He struggled to support his wife, Arlene, and their three children. He worked as a doorman, a cab driver -- even a clown. Finally, in 1971, he was offered the role of Hawkeye Pierce in a television series based on the film M*A*S*H*, the role of a lifetime, but he almost turned it down.
He loved the script and character, but didn't want to work in California while his family was in New Jersey. "Well, I thought this is great. This is one of the best things I ever read. But it's too bad I won't be able to do it, because it would be shot in California and we lived in New Jersey and our children were just entering high school."
Trying not to disrupt his children's education, Alda spent the next eight years commuting from Los Angeles to New Jersey.
M*A*S*H*, of course, was a smash. Its final episode was watched by more than 100 million households. And Alda used the show to pursue not only his passion for acting, but also for writing and directing.
He became one of the most recognizable people in the country, but he was a reluctant star. With his home base in Long Island, for decades, Alda has managed to keep his life remarkably "un-Hollywood." He credits this in no small part to his wife of 48 years, Arlene.
But what's behind their lasting marriage? "The only answer that I can give you is that we love each other," he said.
"Respect is the gigantic thing, where you have fun together, just being -- just being pals. And when you got all of those things together, then you're in clover."
And now Alda has captured some of that wisdom in his new book. But he almost missed his chance to share his life lessons when he nearly died two years ago while hosting the public television show "Scientific American Frontiers" in Chile.
He needed emergency surgery for an intestinal blockage. He recovered but he has faced other health issues -- among them anxiety and depression -- and he is equally candid about them in his memoir.
Alda's journey has contained its fair share of challenges and triumphs and he has finally been able to come to peace with his mother and her lifetime of illness.
It was a simple item in his mother's safe deposit box after she passed away that gave him comfort. He found an old photograph of himself as a boy. "On the edge it says, 'My beloved son, Allie.' And I mean, that was a very important moment for me, because I saw through all of the psychosis, all the illness, the mental disorganization. And I saw through to this woman who loved her boy."