This has never been confirmed.
Marilyn met Bobby on these occasions:
On Thursday 1st February 1962 Marilyn attended a party celebrating Bobby’s goodwill tour of Japan at Pat (Kennedy) and Peter Lawford’s home. Edwin Guthman commented on the way Marilyn and Bobby were behaving that evening. Stating that there was not “the faintest overtone of romantic of romantic interest on his side or hers.”
He later stated that “I travelled with Bobby, day and night for five years and I never saw him pay attention to anyone but his wife.”
Milton Ebbins, who had escorted her there, also took her home. Rumours began spreading after this meeting which prompted Jean, Bobby’s sister, to write to Marilyn sarcastically stating, “I understand you and Bobby are the hot item!”. Which later was mistakenly passed off as being a serious observation. Jean later stated that it was “ridiculous” to take it other than a joke.
Marilyn even wrote a letter to her ex-stepson Bobby stating “Oh, Bobby, guess what: I had dinner last night with the Attorney-General of the United States, Robert Kennedy, and I asked him what his department was going to do about Civil Rights and some other issues. He’s very intelligent, and besides all that, he’s got a terrific sense of humor. I think you would like him. Anyway, I had to go to this dinner last night as he was the guest of honor and when they asked him who he wanted to meet, he wanted to meet me. So, I went to the dinner and I sat next to him, and he isn’t a bad dancer either.” Records show she went home alone in a limo.
On Wednesday 27th June 1962 Marilyn wanted Peter and Pat Lawford, as well as Bobby, to view her new home. After dinner at the Lawfords’ home, the attorney general’s driver took her back to Fifth Helena Drive. Eunice Murray, Marilyn’s housekeeper, stated that “they all came to look at the house. She certainly didn’t go sneaking around with Mr Kennedy or have a love affair with him!
On Saturday 19th May 1962 Marilyn was present to perform Happy Birthday for Bobby’s brother, John. After her world famous performance, Marilyn (as well as her ex-father-in-law Isidore Miller and Pat Newcomb), the Kennedy brothers and other stars went to the home of Arthur B. Krim, where the only photograph of Marilyn Monroe and the two Kennedy brothers was taken. Milton Ebbins took her home at 2 am.
All other dates can be dispelled and proven to be incorrect. Should there be a date on which you may believe Marilyn and Robert were together, please let me know and I will investigate this for you.