FORT LAUDERDALE, Fla. — Jeb Bush and his aides had envisioned a big, inclusive, high-minded speech about race on Friday in his home state of Florida, a chance to bring his message of colorblind opportunity to a prestigious group of African-American leaders.

In a rare gesture of bipartisanship, Mr. Bush even planned to warmly quote President Obama, usually the object of his derision.

Then Hillary Rodham Clinton stomped all over those plans.

In a biting surprise attack, delivered as Mr. Bush, the former Florida governor, waited backstage here at the annual convention of the National Urban League, Mrs. Clinton portrayed him as a hypocrite who had set back the cause of black Americans.

It was an unexpected moment of political theater that seemed to presage what could be a bitter general-election rivalry between two of the biggest names in American politics.