But that hasn't stopped the steady stream of questions he fields from reporters and voters alike. They usually go something like this: How are you different from your father and brother?
As he travels the country as a potential candidate, Bush, who served as Florida's 43rd governor, hasn't run from the family name -- but he's careful not to run on it either.
Before he's even a declared candidate, here's a look at how he has handled the questions about the Bush dynasty:
In New Hampshire last weekend, Bush noted the challenge of differentiating himself to voters, even joking he'd have to prove he wasn't running to "break the tie" between the Bush and Adams family. (Those families, along with the Roosevelts, boast two presidents apiece.)
"I have to prove I'm not running for president ... trying to break the tie between the Adams family and the Bush family," Bush said to laughter and applause last week at the Snowshoe Club in Concord, New Hampshire. "It really isn't my motivation, but I have to prove that."
Back to the Future
"Look, the circumstances for today are different than they were in 2000 and certainly different than they were in 1988," Bush said in New Hampshire last week. "And so there's a whole new set of challenges, a whole new set of opportunities."
Just Say No
Bush gave one reporter little to work with in New Hampshire when asked to provide examples of divergent positions from his brother.
"No, I certainly don't [want to give examples] -- absolutely not," Bush said. "I've got no interest in that."
He added that voters will "have that chance" make comparisons if he becomes an official candidate.
Keep Calm and Carry On
But that might not be enough for some voters, as Bush learned earlier this month, after a breakfast in Colorado Springs with retired generals and military leaders.
"Shame on you!" one voter who identified himself as a Republican shouted. "We've had enough Bushes!"
Bush responded with an abrupt nod.
"Take care," he replied.
ABC News' Jordyn Phelps, Tom Thornton, and Michael Falcone contributed to this report.