His father is Jeb Bush, the former governor of Florida; his uncle is former President George W. Bush.
When he was just 12 years old, he led the Pledge of Allegiance at the 1988 Republican Convention that nominated his grandfather, former President George H.W. Bush.
Now at 37 years old, after a career in law and real estate and service in Afghanistan, he's decided to join the family business.
Bush told CBS News' Chip Reid, that his uncle, the former president, told him he thought he would be good at politics.
"He's always thought that I would be good at it, but in terms of doing it for the right reasons, that's what the consensus was," he said. "Whether it was him or my grandfather or my dad is, you've got to do this with a servant's heart."
While he's running for Texas land commissioner, which manages the state's oil rich public lands, he sometimes sounds like he's got bigger things in mind in his stump speech.
Yet, he told Reid that he doesn't let himself imagine himself as the third Bush president.
"I would love to be a public servant to this great state and I would like to leave everything on the field," he said. "Give 110 percent to the state and we'll see where it takes me."
Bush said his goal is to appeal to all Republicans, from the mainstream to the Tea Party. He's a strong supporter of business and deeply conservative on abortion and gun rights.
His mother was born in Mexico and he feels most Hispanics are, at heart, conservative. He's frustrated with the Republican Party's failure to reach out.
"We don't need to change our conservative values to win the Hispanic vote. We need to change our tactics," he said.
Even with her grandson jumping into
politics and her son, Jeb Bush, contemplating a run for president in 2016, Barbara
Bush recently took on the role of family naysayer during a recent interview.
"If we can't find more than two or three families to run for higher office, that's silly. Because there are great governors and great eligible people to run," she told C-SPAN last month. "There are a lot of ways to serve, and being president is not the only one, and I would hope that someone else would run."
Bush said he talked to her after her interview.
"She said, 'Well, I may have been talking about other Bushes, but not the next Texas land commissioner," he said. "And she clarified her statement after the fact was to say that 'I think ... my dad Jeb Bush would make a fantastic president, but there are also other great people in our country.'"
He said he'd like to see "a strong conservative voice rally this party together," which would be someone like his father.
Bush says there's one big downside to running for office now, which is time away from his 8-month-old son Prescott.
When asked when Prescott would
be out helping on the campaign bus, he said "hopefully sooner rather than
later. Start 'em young."
To see Chip Reid's full report, watch the video in the player above