The Washington Post on Thursday was not immediately able to reach the three women for comment.
The moment, captured in a video shared to Facebook, raises questions about a cultural moment in which some people feel comfortable saying they don't regret using a racial slur.
In the video from Bonefish Grill, Goodman waves at the camera and smiles in an exaggerated fashion when she sees Lekesha Shaw and Chanda Stewart filming her while she talks with a restaurant employee. Goodman then walks over to the women and pulls out her own cellphone as if to film them.
"I've got really good friends that are black, and I love them," Goodman tells the women.
"We never said anything about colour," one of the other women says from behind the camera.
Goodman tells Shaw and Stewart that they're too loud, and Shaw responds that her money is as good as Goodman's. Then, Goodman calls Shaw "stupid" and uses the n-word.
One of the women behind the camera sarcastically tells Goodman that she should call her black friends that word.
"They're not like you!" Goodman replies.
Shaw later told WRAL-TV that it didn't matter how Goodman thought Shaw and Stewart should have been acting in the restaurant.
"If I was standing on the table with three heads in a purple jumpsuit, nothing justifies you to come to my table and call me" that, Shaw told WRAL-TV.
Goodman posted on Facebook on Wednesday to offer an apology to her family, friends and other people at the restaurant that night - but not to Shaw and Stewart. Goodman wrote that she was "ashamed" of her behaviour, but she called Shaw, Stewart and their third companion "rude, loud, obnoxious black women."
"The TV reporters came to my house today as they found out my name which that could only happen if the restaurant gave them my information," Goodman wrote, according to WRAL-TV. "The women taped me and apparently shared the video all over social media. I suffer from extreme anxiety which is not an excuse. I am ashamed of my actions."
A spokeswoman for Bonefish Grill told The Washington Post that the company "does not tolerate hate speech or disrespect" in its restaurants.
"Our team takes this seriously and is providing additional training to our staff for situations such as these that escalate quickly," spokeswoman Elizabeth Watts said in a statement. "We are saddened by what happened and are committed to doing everything we can to ensure guests get the courtesy and respect they expect and deserve - every time."
Stewart wrote on Facebook alongside the video that "The climate of the country today has some people thinking whatever they feel . . . they can say. The reality is if we were to retaliate with this same kind of hate and ignorance we would be called 'angry black women.' "