Martin McGuire, 38, from Hamilton, was travelling at 51mph on a 30mph stretch of road in Motherwell, North Lanarkshire, Scotland, when he hit Abbie Mclaren.
McGuire is the cousin of Abbie’s father, John Mclaren, who was in the passenger’s seat at the time of the accident on February 12.
Abbie, a pupil at Dalziel High School, had just stepped off the bus when she was hit by the Citreon D3.
Judge Lady Scott also handed McGuire an eight-and-half-year driving ban as she sentenced him for causing death by dangerous driving at the High Court in Edinburgh.
She told him: “Abbie Mclaren was 12 years old. She was a child with her whole life ahead of her.
“She was well-loved by her close family, especially her mum, brothers and sisters and her grandparents.
“All have been left devastated and will be forever bereft.”
The court heard that Abbie did not actually know McGuire and did not have any contact with her father.
McGuire tested negative in a breath test but admitted to having no licence or insurance.
The trial was also told he’d never been giving a full licence, but held an expired provisional licence.
Abbie was thrown into the air onto a nearby parked car when she was hit, suffering multiple fractures and dying in hospital the next day.