“This will be the scariest thing that’s happened to us in 50 years,” said Lawrence Wilkerson, chief of staff to Mr. Powell when he was secretary of state. “Bolton is several things, none of them good. He’s an absolutely brutal manager, treats people like dirt. The stories that have come out are accurate, but they don’t go far enough. And he’s also possessed of some views that are just revolting.”

Revolting to his adversaries or refreshing to his admirers, his views are no mystery to anyone who follows him on Twitter or Fox News. In a town of cautious talking points, Mr. Bolton, like Mr. Trump, finds no virtue in subtlety. “China’s jived us for 25 years.” The Iran nuclear deal “must be ripped up.”

The North Koreans are the “biggest con men in the world,” and their planned talks with South Korea could be a “propaganda stunt” to buy time. “Question: How do you know that the North Korean regime is lying?” Mr. Bolton asked recently on Fox. “Answer: Their lips are moving.”

When on another occasion the Fox host Tucker Carlson said the ouster of Saddam Hussein in Iraq had empowered Iran, Mr. Bolton dismissed him. “No,” he said, “because I think your analysis is simple-minded, frankly.”

“He has a very provocative style,” said Stephen J. Hadley, who was Mr. Bush’s national security adviser. “That’s why he was great on Fox. That’s why he was great on the speaking circuit. He loves to provoke. He loves the combat.”

Mr. Hadley, Ms. Rice and other Bush veterans privately cautioned against Mr. Bolton being named deputy secretary of state when Mr. Trump took office. Mr. Hadley declined to discuss that last week, but like other prominent Republicans who do not subscribe to Mr. Bolton’s style or philosophy, he has reconciled himself to the new appointment.

“You can’t fault the choice,” Mr. Hadley said. “This is a very smart guy, very well educated, very well experienced and knows how to work the system.”