During a swing this week through eastern Iowa, former Florida Gov. Jeb Bush stepped up his rhetoric against the political establishment, seeking to catch up to the outsider candidates leading the GOP field.

“I’ve never lived in Washington, never been part of Washington,” the former two-term governor said Wednesday at a coffee shop here. “I just have the skill set to disrupt the beast.”

Mr. Bush, who relishes discussion of policy and counts two former U.S. presidents as family, is struggling to be treated like a renegade. An anti-Washington joke he told about 500 people Tuesday night at a Republican Party dinner in nearby Bettendorf fell flat. “He can pitch himself as an outsider but I don’t know if he can sell it,” said Wylie Pillers, an attorney who attended the GOP dinner and praised Mr. Bush as “levelheaded,” “coherent” and “not extreme.”