She said the two had finished dinner and were in a car for what she thought was a ride to an office building.
"Instead of going into the offices he suddenly reached over and he put his hand on my leg, under my skirt toward my genitals," she said.
"He also pushed my head toward his crotch," she added.
She said she asked Cain what he was doing and recalled he replied, "You said you want a job, right?"
Bialek is the fourth woman to say that Cain engaged in inappropriate behavior during his time at the helm of the restaurant group.
Two women who worked there 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.
Still, some remained solidly behind the former pizza executive, unmoved by Bialek's account. They pointed to the presence of Allred — a high-profile attorney with Democratic ties — as proof the claim was a partisan smear.
"The fact that she's involved removes all credibility," Georgia Christian Coalition president Jerry Luquire said. "If he says he didn't do anything than I believe him."
For Cain's core supporters — tea party activists and evangelical voters — distrust of the media is high. And the accusations against Cain only seemed to galvanize their support.
With that in mind, Cain's leading Republican rivals for the White House steered clear of he scandal on Monday declining to comment.
But there was also evidence the latest allegation as well as the cumulative toll of multiple women making claims could erode Cain's support.
"Oh," exclaimed South Carolina GOP Chairman Chad Connelly said when told details from Bialek's news conference.
Voters in his early primary state, Connelly said, will tune into character questions in a state where the last governor tearfully confessed an affair and the current governor faced unproven allegations from two men that she had affairs.
"Our voters in South Carolina care about character and if the allegation are proven out, our voters care about moral attitude," Conley said. "Character does matter, despite what the Clinton folks tried to tell us years ago," he said.
Associated Press writers Steve Peoples in New Hampshire and Jim Davenport in South Carolina contributed to this report
Follow Shannon McCaffrey at www.twitter.com/smccaffrey13
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