She described the man as about 6 feet tall, white or Hispanic, with a medium build. He had a ponytail and was wearing a floppy hat and sunglasses. She said she begged him not to hurt them and just take what he wanted, but what he wanted was for her to start driving.
"He just said drive to the bank,' she said. "He didn't raise his voice, he wasn't angry, wasn't yelling, wasn't frantic."
She said he seemed to know what he was doing. She didn't want to try to yell for help because her son was strapped in the car seat and the man was pointing his gun at him.
After being ordered to an ATM, Jane Doe withdrew all the money she could -- $600 -- and hoped the man would let them go, she said. Instead, he told her to drive to a remote spot where he ordered her out of the car. He then handcuffed her wrists and used plastic zip ties to bind her feet and her neck to the headrest in the rear seat next to her child, she said.
He then pulled out onto the highway, in what Jane Doe said was the worst part of the ordeal.
"I remember seeing people in cars passing me and just wondering how no one knows, you know, that this is happening to us," she said. "No one knows that there is this horror going on inside this car. No one knows that I'm going to die today."
But in the hour or so they were together, driving and briefly conversing, Jane Doe said she somehow sensed a change in her abductor. Once cold and calculating, he slowly warmed to her. Eventually, she said, he turned the SUV around and returned to the parking lot. Leaving the engine running, he got out and took her driver's license.
But before he left, she said, he gave her a warning: He'd come back for her if she described him to the police.
Jane Doe said she was able to slip her feet through her handcuffed wrists, pop the headrest to free her neck and maneuver into the driver's seat. Feet still bound, she drove to a nearby valet stand where the police were called, she said.
But, she said, police didn't seem to believe her story. She said they made insinuations that her account didn't make sense, and that she might have been seeking attention.
"Why would I do this for attention?" she asked. "I'm with my child. I'm like, 'I didn't zip tie myself and handcuff myself.' I'm like 'I had marks up and down my neck with blood ... and I did that to myself?'"
The police said it's not that they weren't sympathetic, but that it's their job to be skeptical.
"Unfortunately, I wish it weren't this way, but not everything we are told is the truth," Duggan said. "We had some concerns about her story. ... Some of it didn't add up."
The detectives wondered how Jane Doe could have gotten out of the restraints in the way she'd described. They also initially found no proof she went through the highway toll booths, as she'd claimed. Finally, she failed a lie detector test.
But now, after investigating the case, police said they believe Jane Doe.
Still, during the investigation, the police issued a news release that contained only the details they'd been able to confirm. The release described Jane Doe's case as "an alleged armed robbery" and said nothing about the abduction or holding a gun to a child's head.
"They blew it," said Randy Schultz, editorial page editor of the Palm Beach Post.