"I heard about Harvey and I was afraid of him," Bullock told The Sunday Times in an interview published this weekend.
The actress, who stars in the all-female heist movie "Ocean's 8," also described one unwelcome experience early in her career with a person of authority who was not Weinstein. "I learned early on to shut things off so those things didn't come my way," she said.
Bullock didn't go into detail about the incident or name the individual involved, but said that she first tried deflecting the situation with humor. When that didn't work, she asked to be fired. It's not clear if this ended up happening.
The actress has previously said that she nearly quit acting earlier in her career after having a "wake-up moment" regarding sexual discrimination in Hollywood.
When it comes to Weinstein, who co-founded Miramax film studio, Bullock told The Sunday Times that she heard rumors about sexual encounters that painted women in a poor light and him in a powerful one.
"People would say, 'Well, you know how she got that role? She fucked Harvey.' I would say, 'Shut the fuck up. You don't know that.' Then, later, to find out that woman was brutally attacked," she said. "They didn't sleep with Harvey. Harvey wanted you to think that."
Weinstein pleaded not guilty earlier this month to rape and sexual assault charges. More than 70 women have accused him of sexual misconduct.
Bullock said it was "amazing" when women began speaking out about harassment and assault as part of the MeToo movement. Still, she said she had concerns that their accounts could backfire and hurt the accusers, which has happened before.
"We're in such uncharted territory right now. I've seen a lot of fear and a lot of men of a certain generation not understanding," she said.
Read The Sunday Times' full interview with Bullock here.