But his efforts to capitalize on his résumé and reputation have thrust him into situations that may prove challenging to explain should he mount a Republican campaign for the White House. Records and interviews show, for example, that Mr. Bush participated in the fevered, last-ditch efforts to prop up Lehman Brothers, a Wall Street bank weighed down by toxic mortgage-backed securities. As a paid adviser to the company in the summer of 2008, he met with Carlos Slim Helú, a Mexican billionaire, as Lehman sought to persuade Mr. Slim to make a sizable investment in the firm, emails show.

Mr. Bush sat on the board of Swisher Hygiene, a soap maker, at a time when, its executives acknowledged, their financial statements were unreliable and their accounting practices inadequate. That admission contributed to a plunge in stock price that has wiped out more than three-quarters of Swisher’s value and touched off a wave of shareholder lawsuits. Several have named Mr. Bush as a defendant, accusing him and fellow board members of insufficient oversight.

And in a stint that could complicate his appeal to conservatives, Mr. Bush serves as a paid director to Tenet Health Care, the giant hospital owner, which supported President Obama’s Affordable Care Act, aggressively encouraged Americans to sign up for insurance under the program and trumpeted the legislation as a boon to the company’s finances.

The path from public service to private riches is well trodden by politicians of both parties. But, even by that measure, Mr. Bush took an aggressive and expansive approach to making money.