The 54-year-old former US Open finalist told BBC Radio 5 live's Sportsweek programme that Nastase often asked her if she was a virgin.
"Whenever I saw him at any tournament he would ask me the same question," she said. "This man has not been respectful of women for a long, long time."
Nastase was thrown out of Great Britain's Fed Cup tie in Constanta after an extraordinary meltdown that saw him hurl foul-mouthed abuse at the British team and journalists.
Nastase was already under investigation by the International Tennis Federation (ITF) after making an apparently racist comment about Serena Williams' unborn baby at Friday's press conference and asking British captain Anne Keothavong for her room number.
Then on Saturday, with Johanna Konta leading Sorana Cirstea 6-2 1-2 in the second rubber of the World Group II play-off, Nastase became embroiled in a row after Keothavong complained about noise from the crowd.
The 70-year-old former world number one was heard to say to umpire Jaume Campistol: "What's your f***ing problem?" He then called Great Britain captain Anne Keothavong and Konta "f***ing bitches".
Nastase was sent off the court by tie referee Andreas Egli, who he called a "f***ing a***hole", and was eventually escorted out of the Tenis Club IDU by security.
"When I got older, perhaps 20, and he asked me for about the 30th time, I said, 'would you please stop asking me that?'," said Shriver.
"Sort of to his credit, he never asked me again. I set a firm boundary and he stopped."
Shriver did not report Nastase's behaviour and added: "You want the punishment to match the crime and he behaved really badly.
"I think it has all gone too far, I think it is over now. I think he is done as a coach, certainly in any formal setting.
"Everybody has a couple of different sides to their personality and certainly not all of Ilie Nastase is evil and mean and sexist. But unfortunately he does not have a filter and there is a side that is, so he can't coach women players any more."
