The Tennessee Bureau of Investigation said the suspect, Tad Cummins, 50, also did online research about his car "to determine if certain features could be tracked by law enforcement."
"We need you home," Elizabeth's sister, Sarah Thomas, told ABC News today. "Whatever he's telling you is a lie ... just call or text us whenever you can."
Amid the desperate search for the victim, the TBI released a photo today showing Elizabeth and Cummins together in their Culleoka school in January. The photo was taken days before Cummins had "alleged inappropriate contact with her," the TBI said.
One of her schoolmates reported seeing them kiss in his classroom on Jan. 23, according to a school district investigative report, but Elizabeth and Cummins denied the claim.
The TBI said that Cummins "may have been abusing his role as a teacher to groom [the teen] ... in an effort to lure and potentially sexually exploit her."
Thomas told ABC News that Elizabeth was bullied in school by students and teachers after the reported kiss and told her, "I just have to get away. We have to get away."
"I can't handle this anymore ... all the teachers, all the kids constantly saying mean things. I can't handle it," Thomas recounted.
She said her sister woke her up urgently the day she disappeared and made her promise to call the police if she was not home by 6 that night. Thomas said Elizabeth sounded "serious," not happy. "She's not a serious person."
When Elizabeth didn't come home, Thomas was scared.
"I felt like it was my fault," she told ABC News. "Maybe if I would have done something" that morning and didn't fall back asleep, "I could've stopped her."
But Thomas said she doesn't think Elizabeth knew she was leaving that day and that her sister wouldn't leave without at least hugging her.
"If she gets sick, he can't do anything ... She doesn't have a way of getting to the doctor," Thomas said.
She also said her younger sister is "not a camper." She hates the woods and is scared of snakes and spiders, Thomas said.
An attorney for the school district has not responded to ABC News' request for comment about the bullying claims.
As authorities search for the pair, authorities say Cummins is believed to be armed and that Elizabeth is "in imminent danger."
Authorities said neither Elizabeth nor Cummins has been in touch with family members.
TBI spokesman Josh DeVine told ABC News about 600 tips have come in as of today, which he called "substantially low." And there are still no credible sightings of the duo, which DeVine says is very rare.
Cummins' wife, Jill Cummins, pleaded with her husband Friday to "come home." "I had no idea my husband was involved with anything that has led to all this. My heart breaks for the family of Beth Thomas," she said. "Tad, this is not you. This is not who you are. We can help you get through this ... Your family wants their poppy back. Please do the right thing and turn yourself in to the police and bring Beth home."
In an interview with ABC News Monday, Elizabeth's father, Anthony Thomas, pleaded with his daughter, "Please let us know you are all right and please come home to us."
Thomas family attorney Jason Whatley told ABC News that Cummins was "taking advantage” of his student and "manipulating her into leaving with him."
"We are very concerned about the control that he has over her," Whatley said. "We believe that is 100 percent the reason why she is missing at this point. He is the problem. She is not. She's a child. She's a victim."
Cummins is described as 6 feet tall and about 200 pounds. He may be driving a 2015 silver Nissan Rogue with Tennessee license plate number 976-ZPT.
Elizabeth is described as 5 foot 5 and 120 pounds. She was last seen wearing leggings and a flannel shirt.
Authorities are asking that anyone with information call 1-800-TBI-FIND and that anyone who sees a car with a Tennessee license plate 976-ZPT call 911. A $1,000 reward is available for information leading to Cummins' arrest.
ABC News' Eva Pilgrim and Janice McDonald contributed to this report.