Early on in the exclusive sit-down, the former president expressed a clear-eyed support for the news media, saying a free press was "indispensable to democracy.
"We needed the media to hold people like me to account," Bush told TODAY'S Matt Lauer.
"Power can be very addictive and it can be corrosive, and it's important for the media to call to account people who abuse their power."
Read more from Today:
Chuck Todd: John McCain is concerned Donald Trump 'crossed the line' about media
SodaStream recalls 51,000 bottles due to explosion risk
Can you answer these 27 tough (and bizarre) job interview questions?
Bush was asked about the media's role in light of President Donald Trump's recent characterization of the media as "enemies of America." He noted he spent a lot of time during his two terms trying to convince Russian President Vladimir Putin to embrace an independent press.
"It's kind of hard to tell others to have an independent free press when we're not willing to have one ourselves," he said.
Bush also addressed the controversy over Trump advisers and the role they may have played in the scandal involving Russian hackers who tried to intervene in the election, saying he would leave questions about whether a special prosecutor should investigate up to the Senate intelligence committee leaders.
"I think we all need answers," he said, noting that he was not a lawyer so, "I'm not sure the right avenue to take."
Bush, the last Republican to occupy the White House before Trump, also was asked about President Trump's controversial executive order that banned immigrants from predominantly Muslim nations.
Asked pointedly if he favored or opposed the policy, Bush said, "I am for an immigration policy that is welcoming and upholds the law."
Bush won the 2000 presidential election after one of the most contentious and controversial decisions in American history. He took office after a divided Supreme Court ruled over a dispute involving a contested recount in Florida.
Bush also returned to the show to discuss his new book, "Portraits of Courage: A Commander in Chief's Tribute to America's Warriors," a collection of portraits of some of the military veterans he has met.
Proceeds of the book will be donated to the George W. Bush Presidential Center, a non-profit organization that helps post-Sept. 11 veterans and their families make successful transitions to civilian life.
The portraits are also currently on display as part of an exhibition at the George W. Bush Presidential Center in Dallas, Texas.
—By Eun Kyung Kim, TODAY.com.
See more News from The TODAY Show at our Facebook and Twitter.