Bush formally launched his bid at Miami's Dade College on Monday, a diverse university in Florida chosen to transmit the message that he aims to run an inclusive campaign.
The son and brother of two former presidents, Bush, 62, was expected to highlight his own successes as a two-term governor of Florida, where he claimed high job growth and other economic and social gains.
Al Jazeera's Andy Gallacher, reporting from Bush's campaign launch, said Bush appeared to distance himself from the family legacy in launching the "Jeb 2016" campaign.
"He has the name recognition but that can also hinder him on this campaign. Remember, this is the candidate who was supposed to suck the oxygen out of the room, the man with the name recognition, the man with the huge war chest," our correspondent said.
"Many of the other candidates running for the nomination are younger, fresher and more conservative than Jeb Bush is. When he was governor here, he was considered conservative.
"But in the 13 years since he ran for office the party has moved to the right, making him more of a moderate these days but he says he can reach out to voters the Republicans don't normally get."
Not all to plan
While Bush has been said to have been running a "de facto campaign" for the past six months, not everything has gone to plan.
"Just a couple of weeks ago, he tripped over a question about Iraq and what he would have done in the situation his brother George Bush was in and also this last week, many of the key campaign members of his team were fired and replaced with other people," Al Jazeera's Gallacher said.Strongly pro-business and anti-abortion, Bush has resisted party orthodoxy, making far-right voters wary of his support for immigration reform, federal education standards and a willingness to hike taxes as part of a deficit-cutting deal.
Fluent in Spanish, he insists legalising millions of undocumented workers is the immigration debate's "grown-up plan" and will fuel economic growth, unlike the mass deportations advocated by some hard-liners.
Nationally, Bush is placed at the top of most Republican polls, but he is not the dominant figure many had expected.
Hillary Clinton is the front-runner on the Democratic side, with no current close competition.
While many Americans were lamenting the prospect of another Bush-Clinton presidential race and criticised the country's dynastic politics, plenty of analysts were saying that they expected that neither candidate might still be in the race in the primaries in more than a year, our correspondent said.
Source: Al Jazeera And AFP