When you have major donors who have been given ambassadorships, in some cases in two previous Bush presidencies, that type of cronyism may make it hard for other 2016 GOP hopefuls to raise the money they’ll need to compete in what could be a long, expensive primary if Jeb Bush opts to run.

Early signs suggest that devotion to the Bush clan may trump newer relationships. Two leading members of Mr. Rubio’s Senate fundraising team—lobbyist Charlie Black and Dirk Van Dongen, the head of a trade association—have suggested they would lean toward the former governor if both men pursued the Republican presidential nomination.

Jeb seems to be wasting no time in cozying up to individuals who helped finance his brother’s or dad’s campaigns, if not both. Add in the funding structure he built for himself in Florida and it creates a formidable juggernaut. It also may cause some to question if the Bush family doesn’t have too strong a grip on the Republican Party, or if the GOP is still a party based on democratic principles, or simply one in which cronyism and big dollars allows one family, or person to simply but their way to the top.

That legwork allowed Mr. Bush to hit the ground running. After posting his plans last Tuesday on Facebook and Twitter, he called Mr. Rubio, associates say. He then huddled the next day with roughly two dozen friends and some loyal donors in Coral Gables, Fla. He wrapped up the week with meetings with other fundraisers in Dallas and Chicago, while reaching out to donors elsewhere. Other trips are in the works, including one to Washington.

The Florida gathering illustrates how Mr. Bush would benefit from his family’s legacy. The event included a number of donors who supported Mr. Rubio’s 2010 Senate race and have given money to his PAC. But their allegiance to the Bush family dates back decades. Tampa-area developer Mel Sembler, for example, met Mr. Bush when he rented space for a campaign office to his father in 1979. George H.W. Bush later appointed Mr. Sembler as ambassador to Australia. George W. Bush tapped him to be ambassador to Italy.