The pedestrian was hit at the Texaco garage on Roman Farm Road, Hengrove, on Tuesday evening and trapped by the car until it stopped on Creswicke Road.
Shakrun Islam, 30, of Chipping Sodbury, is due before Bristol Crown Court on Friday. He was remanded in custody.
The victim, Kyle Clarke, died at the scene from his injuries.
His mother, Helen Stockford, said in a family statement: "We would like to thank the public and the emergency services for all their support on Tuesday night.
"We would ask the media for privacy at this time to allow us to grieve in peace."

Sakho, who is currently on loan at Crystal Palace, tested positive for the fat burner higenamine in March 2017 and served a provisional 30-day suspension.
Uefa dismissed the case in July.
European football's governing body blamed "gaps in communication" between Wada and two of its laboratories.
A Uefa report released on Thursday said it was "clearly not possible" for anyone to tell whether higenamine is a prohibited substance by reading Wada's banned list.
"The fact that the Cologne laboratory tested for higenamine but had to check with Wada before making a determination indicates a problem, as does the fact that the Lausanne laboratory does not test for it," it added.
"The onus is clearly on Wada to communicate to its laboratories what is and what is not on the prohibited list.
"There are clearly gaps in communication with regard to higenamine, something which also tends to support the suggestion that Wada's own internal procedure and analysis in respect of this substance is incomplete."
Sakho, 27, admitted taking the substance without Liverpool's knowledge but contended it was not on the banned list, which was supported by the report into the case by Uefa's control, ethics and disciplinary body.
The France international has not played for Liverpool since testing positive and moved to Palace on loan in February.
A man has appeared before magistrates in Bristol charged with murder after a man was knocked down and dragged under a moving car.
[NEXT_CONCEPT]
Liverpool centre-back Mamadou Sakho was suspended last season for taking a substance that was not on the World Anti-Doping Agency's (Wada) banned list, according to a Uefa report.