"Inspiration is seeing acts of compassion that really are the backbone of the great American scene," he said, adding that he hopes the children take away from the experience "that God continued to provide loving people in their lives, so that they don't get lost and so that they realize that the American experience is made as much for them as it is [for] anybody else."
Throughout his presidency, Bush has supported faith-based programs, and said he hopes Obama will continue some of those initiatives.
"I think he knows that in certain communities, in order to help achieve a national objective, there needs to be something more powerful than government, and you can find that there's something more powerful than government on nearly every street corner, in a house of worship," Bush said. "And if you say results matter more than process, then you'll recognize the great efficacy, as well as the love, of a faith-based program."
He also told McFadden about the role of the president as the "comforter in chief."
"Well, one of the things, as president, you see a lot of hurt," he said. "And the great thing about America is most people deal with the difficulty with great strength and courage and determination. The 'comforter in chief' usually is the comforted person when you talk to Americans who overcome adversity."
His remarks echoed those from a recent interview with ABC News' Charles Gibson, when Bush said that, despite dealing with tragedy, he has found his time in the White House to be joyful.
The president told McFadden that his faith has been one of many sources of strength in his life.
"I've got a fabulous wife ... my mother and dad gave me unconditional love," he said. "I get strength from my friends, who were my friend before politics, during politics, and they will be my friends after politics, regardless of what took place during politics. And then I get my strength from just fellow citizens."
After the event in North Carolina, the president told McFadden that he always enjoys meeting with young people, and reflected on his own experience raising two daughters in the White House.
"I have done it, I have lived through, and I am a better man for it," he said, adding how proud he is of daughters Barbara and Jenna.
"They both have been good stewards and they are learning what it means to serve something greater than themselves, and it makes their mom and dad very proud," he said.
While traveling recently in Panama on her last solo trip as first lady, Laura Bush told McFadden that she and the president tried to find a "balance" for their family and said she would advise the Obamas to "err on the side of privacy for children. I think it lets children grow up and make childish mistakes, which, of course, they will out of the limelight. And I think that's really the best."
Watch more of Cynthia McFadden's interview with first lady Laura Bush Tuesday on "Nightline."
When asked if he thinks it's difficult to be a Christian and be president, Bush said, "It's hard to be Christian period, whether you're president of the United States or whatever, because in order to be a true Christian, you have to accept that God's gift is one of grace and there's nothing you can do to earn God's love, God is love and that ... what's hard is take that love and then change your behavior to honor that love."