The prestigious consulting firm, known for its close ties to Gov. Rick Perry of Texas, was orchestrating an extensive effort to remake his image and prepare him for the 2016 presidential campaign.

But that was no deterrent for Jeb Bush. His team hired the firm anyway and quickly made it clear that it wanted undivided allegiance. The company, FP1 Strategies, soon severed ties with Mr. Perry, startling his staff.

Mr. Bush has vowed to run a “joyful” presidential campaign free from the seamier sides of party politics, projecting the air of a cerebral man almost effortlessly drawing together Republicans eager to help him seek the White House. But behind the scenes, he and his aides have pursued the nation’s top campaign donors, political operatives and policy experts with a relentlessness and, in the eyes of rivals, ruthlessness that can seem discordant with his upbeat tone.

Their message, according to dozens of interviews, is blunt: They want the top talent now, they have no interest in sharing, and they will remember those who signed on early — and, implicitly, those who did not. The aim is not just to position Mr. Bush as a formidable front-runner for the Republican nomination, but also to rapidly lock up the highest-caliber figures in the Republican Party and elbow out rivals by making it all but impossible for them to assemble a high-octane campaign team.