The 28-year-old was described as 'no looker' following her straight-sets victory over Sabine Lisicki in the ladies' final on Saturday.
Inverdale said on BBC Radio Five Live: "Do you think Bartoli's dad told her when she was little: 'You're never going to be a looker, you'll never be a [Maria] Sharapova, so you have to be scrappy and fight?'"
According to the Daily Mail, Bartoli responded by saying: "I invite this journalist to come and see me this evening in ball gown and heels, and in my opinion he could change his mind.
"I am not blonde, yes. Have I dreamt about having a model contract? No. But have I dreamed about winning Wimbledon? Absolutely."
Bartoli took part in the traditional dance with men's winner Andy Murray during last night's Champions' Ball in London.