His itinerary for the next several weeks includes stops in the states of Tennessee, New Mexico and Nevada to appear with Republican candidates in this autumn's midterm US congressional elections or help them raise money for their campaigns.
And then he speaks at a dinner ahead of a Republican Jewish Coalition meeting featuring several potential Republican presidential contenders at the Venetian Hotel in Las Vegas.
The hotel is owned by casino magnate Sheldon Adelson, who gave more than US$100 million to Republican candidates in 2012.
Could Bush, 61, the son of a US president and the brother of another, quietly be laying the groundwork for a historic attempt to become the third member of his family to occupy the White House?
When Bush is asked if he will run in 2016, he deflects the question, saying he will decide by the end of this year based on family considerations and whether he thinks he can run "joyfully".
Bush's spokeswoman, Kristy Campbell, declined to comment.
But several people close to him say there are signs that he is seriously considering stepping into the fray. At this point in previous election cycles when his name has surfaced, Bush has told friends, staffers and fellow Florida politicians that he would not run. However, he "has not waved away anyone at this point" for 2016, said a Washington-based Republican strategist familiar with Bush's discussions about the presidency.
To the contrary, the strategist said, Bush has in place an "inner circle" of fewer than a dozen people who are in regular contact with him weighing the pros and cons of running.
"They are at the beginning of a very serious conversation," the strategist said.
A former Bush campaign aide who remains in contact with the former governor said this year's speculation is more warranted than that of previous years.
"I think he's giving it a real, serious look now," said the aide.
Former Republican senator Mel Martinez of Florida, who was secretary of housing and urban development during the presidency of Bush's brother, George W. Bush, said that in Jeb Bush's south Florida base there is a growing belief among political observers that he is leaning toward joining what promises to be a crowded field of Republican presidential contenders.
Republican strategists said that Bush - whose eight years as Florida's governor ended in January 2007 - could change the dynamic of the Republican nomination battle and provide a defining moment for a party struggling with a divide between conservative "tea party" activists and more moderate members of the Republican establishment.
There are no declared candidates yet, but the race for the Republican nomination appears to be shaping up as a contest largely among staunch conservatives favoured by the tea party movement, such as Texas Senator Ted Cruz, libertarian Republican Rand Paul and Wisconsin Governor Scott Walker.
A more moderate potential candidate, New Jersey Governor Chris Christie, has been caught up in a political scandal that has made some Wall Street donors nervous about his prospects.
For big-money Republican donors, strategist Matt Mackowiak said, Bush would represent a marquee name in US politics that could attract the support beyond the far-right Republican base that will be needed to win a general election.
He could also bring enough star power to go up against former secretary of state Hillary Rodham Clinton, who officials in both parties expect to run and win the Democratic presidential nomination.
For pundits, political observers and history lovers, the prospect of a Bush-Clinton battle for the White House would be a dream match-up - a showdown between two branches of America's political royalty.
Recent early polls have suggested that if he were to run, Jeb Bush would be weighed down by lingering attitudes towards his brother, who left office in January 2009 as one of the least popular presidents in US history.
In a Washington Post/ABC News poll this month, nearly half said they "definitely would not" vote for Jeb Bush in 2016 - a level of disapproval matched only by the 2012 Republican nominee Mitt Romney.
Even Bush's mother, former first lady Barbara Bush, has been lukewarm about the idea of another son running for president.
"There's no question in my mind that Jeb is the best qualified person to run for president, but I hope he won't, because he'll get all my enemies, all his brother's," Barbara Bush, wife of George H.W. Bush, said in January. She softened her stance in an interview with Fox News this month, saying that "maybe it's okay" if Jeb were to run.
For a Republican Party desperate to broaden its appeal among the nation's fast-growing and Democratic-leaning Hispanic population, a figure like Jeb Bush could be significant.
He speaks Spanish and his wife, Columba, was born in Mexico. Bush - who won 61 per cent of Florida's Hispanic vote in his 1998 governor's race, according to exit polls - has backed legal status, but not full citizenship, for undocumented immigrants. His compromise drew conservative fire when Bush' promoted his book Immigration Wars: Forging an American Solution in 2013.
Bush headlined a Republican National Committee fundraising lunch in southern California in February and spoke to a group of New York-area business leaders less than two weeks later.
He also appeared in a US Chamber of Commerce advertisement for the Republican candidate in a Florida special congressional election, and campaigned with his son, George P. Bush, who is running for Texas land commissioner.
In the coming weeks Bush will raise money for or appear with a slate of Republicans up for re-election this year.
Some Bush allies reject the idea his recent activity reflects a desire to run for president.
"People who know a lot aren't talking, and the people who are talking don't know. He's made clear he's going to be deliberate and methodical in the way he goes about this," said former Florida congressman Tom Feeney, who ran for lieutenant governor on a ticket with Bush in 1994 and remains close with him.
Several Republican strategists and Bush loyalists said it would take less time for Bush to organise a full-scale campaign team than it would for someone like Walker or Cruz, thanks to his family's experience and connections.
They also dismissed concerns that Bush would have trouble running a modern campaign, given that he has not run for office since 2002 - before the age of Twitter and the tea party.
"Jeb is the exception," said Mackowiak. "The time it takes to build a national finance operation for one of those other candidates? He only has to spend a fraction of that to get his together. ... The clock is ticking for him, it's just ticking more slowly."