WASHINGTON — Stephen K. Bannon, 10 months removed from the job of chief strategist to President Trump and five months after his ouster from the arch-conservative news site Breitbart News, is betting that Bitcoin and other cryptocurrencies can disrupt banking the way Mr. Trump disrupted American politics.

Mr. Bannon won’t reveal very much about his cryptocurrency plans — he worries that the controversy that comes with his name could have a bad impact on projects just getting off the ground.

But he has had private meetings with cryptocurrency investors and hedge funds where he has discussed working on so-called initial coin offerings through his investment business, Bannon & Company. And in his first interview on the topic, he said he had a “good stake” in Bitcoin.

In a small gathering of academics at Harvard University this spring, he even floated the possibility of creating a new virtual currency, the “deplorables coin.” The name is a nod to Hillary Clinton’s description of Mr. Trump’s supporters as “a basket of deplorables.”

