That led to a trip to Washington about a month later, where she recalled that Cain upgraded her hotel room to a suite, and made his unwanted sexual advance.
She said she asked Cain what he was doing, and recalled he replied, "You said you want a job, right?"
Given her experience and those of other accusers, "I want you, Mr. Cain, to come clean," she said. "Just admit what you did. Admit you were inappropriate to people."
She added: "Mr. Cain, I implore you: Make this right so that you and the country can move forward and focus on the real issues at hand."
The denial from Cain's campaign was as unequivocal as the allegation.
"Just as the country finally begins to refocus on our crippling $15 trillion national debt and the unacceptably high unemployment rate, now activist celebrity lawyer Gloria Allred is bringing forth more false accusations against the character of Republican front-runner Herman Cain," it said.
"Mr. Cain has never harassed anyone."
Before Bialek stepped to the microphone, the allegations involved two women who had worked at the National Restaurant Association, both of whom filed sexual harassment complaints.
A third woman told The Associated Press last week that she considered filing a workplace complaint against Cain over what she deemed sexually suggestive remarks and gestures that included a private invitation to his corporate apartment.
A former pollster for the restaurant association has said he witnessed yet another episode involving a fourth woman.
Allred has represented several high-profile clients, including Amber Frey, a witness against convicted California killer Scott Peterson. Allred also represented a woman whom news reports accused of having an affair with golfer Tiger Woods.
"I consider sexual harassment the No. 1 problem in the workplace," she told the AP in an interview last week. "It denies equal opportunity in the workforce. If (women) don't protest it, they'll have to continue to suffer."
Associated Press writers Philip Elliott in Washington and Shannon McCaffrey in Atlanta contributed to this story.
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