John Micklethwait, the editor in chief of Bloomberg News, walked into his Washington bureau on a Friday morning in December with a daunting task: explaining to his political reporters how to cover a presidential campaign when the boss is a candidate.

Addressing roughly 100 journalists spilling out of a glass-walled conference room, Mr. Micklethwait said Michael R. Bloomberg’s entry into the Democratic race had not changed his commitment to skeptical coverage. “We always knew it would be tough,” he told the group. “But we are actually showing what we are: an independent news organization.”

Not every reporter was reassured. Rival candidates had attacked the journalists’ coverage as biased; some sources had stopped returning calls. One reporter said the bureau’s credibility was at stake, citing Mr. Micklethwait’s public memo that Bloomberg News would refrain from “investigating” Mr. Bloomberg and his Democratic competitors.

Mr. Micklethwait said he had been referring to a team of specialized investigative reporters and not the broader political staff, but he declined requests from the journalists in the room to issue a clarification. Many reporters left feeling unsure how to proceed, according to several people who described the previously unreported town hall meeting.