Even though it's been 15 years since Linda Walker Zevallos briefly dated Robert Durst, she tells PEOPLE, "I am still scared to death"

She just wasn’t that into him – and that, she believes, may have saved her life.

When Linda Walker Zevallos briefly dated real estate scion Robert Durst in 2000, she had no idea that he was a suspect in the 1982 disappearance of his wife, Kathie Durst.

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Today, the Dallas-based real estate agent knows that Durst, 71, the focus of HBO’s recent documentary series, The Jinx, was arrested on March 14 and charged with the murder of his friend Susan Berman – and that he was acquitted in 2003 of the murder of his neighbor Morris Black, whom he admitted to dismembering.

“I feel very lucky,” she tells PEOPLE. “I dodged a bullet.”

Zevallos, 64, ended her relationship with the millionaire after just six months. “I just had had enough,” she says. “It was too weird. I just sensed there was something wrong with the guy.”

A Chance Encounter

Zevallos met Durst on a flight from New York to Dallas in March 2000. “He was quite nice on the airplane. He was a good listener.”

But she says he initially lied to her about his background. “He told me he was a labor lawyer,” she says. “He told me he had two daughters who went to Harvard. He also told me that his friend’s wife went missing. Not his but his friend’s.”

When she got off the plane, he asked her to go out with him. “I said, ‘Maybe, but I’m not sure.’ ”

The next day, Durst sent her flowers along with his phone number. “There must have been $500 worth of orchids,” she says. When she called him to thank him for the orchids, he asked her out again, which she politely declined. But when he called her yet again, asking her to go out for lunch, she said yes.

Since all of her friends were married, she says she would take him up on some of his offers to go out but wasn’t interested in a serious relationship with him. “I was just never into him. The only reason I kept seeing him is because he was the one who was pursuing me. He kept calling and calling.”

Concrete Floor

Looking back, things that seemed innocuous then have new meaning today, she says. She remembers stopping by his apartment once on her way to another engagement. “I noticed that there was a room with a concrete floor and an electric saw in it,” she says.

At the time, she didn’t think anything of it. “He told me they were remodeling because they were turning the apartments there into condos,” she says.

Now she wonders why he lied about the floors. She says her friend, Dallas real estate journalist Candace Evans, recently told her that she had spoken to the manager of Durst’s former building. “She told me the manager told her [Durst] wanted a concrete floor because he used a lot of chemicals,” says Zevallos.

Green Ink

While Durst was courting Zevallos, she says, he sent her a handwritten note on stationery from his Wall Street office – the same address found on a letter that Durst sent to Berman that was featured in The Jinx.

She put the letter away and forgot about it until 2008, when she read a story about the now-famous “cadaver” letter that was sent to the Beverly Hills Police Department, telling them there was a dead body at Berman’s address. “It said that said it was written in green ink. Since Durst was a suspect in Berman’s murder, I thought, ‘I have to go look at my letter and see if it was in green ink.’ Sure enough, his letter to me was written in green ink.” She says she contacted the police department about the letter.

Red Flags

As Zevallos got to know Durst, she says, there were times when he could be very nice but “he could also be mean if he didn’t get his way.”

When she told him she couldn’t go to dinner with him because it had snowed and her son was home from school, “he got really mad about it.”

After they hung up, he called back to apologize, offering to take her and her son out for dinner near their house. “He picked us up,” she says. “My 13-year-old son was in the backseat. After we started driving, Robert goes, ‘Oh, I forgot. I’ve got two guns in the backseat.’ And here is my son sitting back there.

“I said, ‘Why are you carrying guns around? Something is going to happen because of that. That is so dangerous.’ ”

While her son says he never saw any guns in the backseat, she says, “It scared me.”

She says Durst lost his temper again when they went out to dinner and she told him she wanted to order the sea bass. “He got mad and said, ‘Well, you can’t have that because I’m having that.’ Then he kind of kicked me under the table. I thought that was kind of mean.”

When she failed to meet him for tennis, she says, “He called me and said, ‘I went ahead and played and charged it to you,’ ” she says. She hung up and called him back, saying, ‘You go back to my tennis club and settle the bill and don’t ever call me anymore.’ ”

It wasn’t until the following March that she learned who Durst really was. “I saw the Today show. They were talking about Robert Durst. They had pictures of him and Kathie Durst and then they were talking about Susan Berman. I was shocked. It was only six months before that I saw him.”

Zevallos says she watched The Jinx and couldn’t believe all she learned about the man who had once courted her so fervently. “I am still shocked,” she says. “Even 15 years later, I am still scared to death.”