On another occasion, the student brought a male friend for a four-in-a-bed session.
Jenkins then took the girl for a drink after a school prom before they went back to her home and had sex with each other and Jenkins' then-partner.
The pupil was then invited to the house with a male friend of hers and the four again had an orgy, a hearing at the National College for Teaching was told.
A professional conduct panel found Ms Jenkins guilty of unacceptable professional conduct and conduct that may bring the profession into disrepute.
Teacher panellist Dr Robert Cawley said: "[The pupil] describes how she had sex with [the man] but cried and had asked for it to stop as she did not want to have sex with a man."
Ms Jenkins attempted to cover up her relationship with the pupil by paying her by-then ex-partner around $24,000 - wholly or partly so he would not report it, the hearing was told.
She later claimed this was to buy him out of the house they shared, but the panel, sitting in Coventry, did not believe her.
Ms Jenkins told the school the man "always threatened to tell the school. I paid him off in the end as he wouldn't leave the house and asked for money to stop him telling."
The girl didn't report Jenkins until she went to university and attempted to deal with what had happened.
In June 2007 the student told staff at her hostel about the relationship but it was not taken further because she was not ready to go through with an investigation. The relationship ended in December 2008.
But in October 2015, she sent a text message to Jenkins, reminding her of the sex at the homeless shelter. Jenkins called it 'the stuff that shouldn't have happened,' but according to the panel's chairman she still tried to re-ignite the relationship. The former student, now in her 20s, finally reported the fling to the school.
Jenkins was suspended and an investigation began, leading to yesterday's decision.
Neighbours at the Jenkins' three-bedroom semi-detached home said yesterday she was 'sex-crazed' and would keep neighbours awake at night.
One said: "Her husband used to complain that she was a total sex maniac. It's common knowledge that she was at it all night. People living closest to her couldn't sleep for the headboard banging against the wall."
Banning Jenkins from teaching for life, Alan Meyrick, on behalf of the Education Secretary, said the relationship was 'only possible because Ms Jenkins was in a position of trust as a teacher".
Jenkins was in Tenerife yesterday but a friend of the family said: "She has four very nice children going on to good careers and it's all a pack of lies. She a wonderful teacher."
Ms Jenkins left the school in July 2015, but continued teaching elsewhere before she was suspended in October that year.
Ms Jenkins was prohibited from teaching indefinitely which means she cannot teach in any school, sixth form college, relevant youth accommodation or children's home in England.
