Caroline Robinson told BBC Radio 5 Live that she told one relative about the first incident but told no-one of the second time because she did not think anyone would believe her.
"I told my grandma... his sister Marjorie, I told her," she said of the first incident at a family party when she was 12.
"All she turned round and said, 'It's only Jimmy, it doesn't matter, I'll sort it out'. She was the one person that I trusted."
Of the second incident, at her own engagement party when she was 15, Robinson added: "I told him to get off, but the music was so loud and people were talking that my voice couldn't be heard.
Copyright: flickr/BBC Pictures"My initial reaction was to close my eyes and just go along with it and when I finished doing what he wanted me to do I just went outside and was sick.
"When I went home I had a bath with the excuse of the cigarette smoke because I don't smoke, and I couldn't wash his smell away."
Asked if she told anyone about what happened at the time, Robinson said: "I didn't, no.
"Who would believe me? Who would believe that Jimmy Savile could be like that?"