DALLAS — The last names Clinton and Bush typically mean political combat of the past, present and potential future. But on Thursday, Bill Clinton and George W. Bush were all charm as they took the stage together here in a bipartisan love fest to promote a joint scholarship program.

Despite their political differences, the two former presidents share a warm relationship, and they occasionally appear together at paid speeches. But they rarely sit down together publicly, much less with a joint appearance that comes as Mr. Bush’s brother Jeb and Mr. Clinton’s wife, Hillary Rodham Clinton, seek their respective party nominations for president.

Before the former presidents took the stage, Jake Harriman, a Marine veteran and one of the graduating scholars, delivered an impassioned speech about the potential only America provides.

“I know two people who are glad he’s not running for president,” Mr. Bush said.

“I know two who are glad he didn’t run earlier,” Mr. Clinton replied.