"This is a premier publication, and everything that News Corp. brings to the table runs the risk of tarnishing that reputation," said Yount.
News Corp. has "not been labor friendly," Yount said, but "honest to God, that is a secondary concern for me."
In The Wall Street Journal newsroom there was a lot of surprise and uncertainty, with the staff learning about the bid through various media reports, sources told ABC News.
The news comes just days after Marcus Brauchli was named managing editor of The Wall Street Journal, replacing Paul Steiger, who has held the top job in the newsroom since 1991.
Neil Henry, a professor at the University of California at Berkeley's graduate school of journalism, said that Murdoch in the past has interfered in the news-gathering role of his media outlets.
"The Wall Street Journal is just a truly wonderful, independent newspaper, and for it to be in the hands of a media titan like Rupert Murdoch does not excite me," Henry said. "I don't believe that media consolidation is good for democracy. You are essentially limiting the number of people and powers that control the news in society. And News Corp. in particular is just a huge, giant of a corporation."
The Bancroft family has a special class of shares that prevents the company from being taken over without its consent. The New York Times, the nation's third-largest newspaper behind The Wall Street Journal and USA Today, has a similar ownership structure.
Shareholders of The New York Times Co. have recently rallied to try to dilute the Sulzberger family's control over the company.
"The Bancroft family … has made it very clear over the years that they treasure the institution that the family has built: the independence, the integrity, the unquestioned quality and commitment to fair and unbiased reporting," Yount said.
Shares of News Corp. fell more than 4 percent Tuesday, closing at $23.10.
Spencer Wang, a research analyst at Bear Stearns, issued a note saying the acquisition is bad for News Corp. because it would increase the company's "exposure to slower growth print assets."
Jennifer Saba, associate editor of Editor & Publisher, said Murdoch "clearly has been wanting this paper for a long time and the question is if the Bancrofts will allow him to have it."
Saba said new owners typically like to make changes, but it is too early to say what, if anything, Murdoch would do.
"If he were smart, he would probably just let it run the way it is running at the moment," she said. "They made a lot of changes, doing deeper analysis with their print edition and breaking a lot of stuff online. They're really on the forefront of online journalism and advertising."
Since 1947, The Wall Street Journal has earned 33 Pulitzer Prizes, journalism's top award. It just won two this year, one for last year's series exposing stock option backdating, and the other for its reporting on China's growing economy.
Besides The Wall Street Journal, Dow Jones owns Barron's, MarketWatch, Factiva, Dow Jones Newswires and local newspapers in Cape Cod, Nantucket, Oregon and elsewhere.