Zachary Williams, 28, was arrested after a pursuit on Friday 24 November that began at about 5.40pm.
Officers on a mobile patrol in Winterstoke Road saw Williams at the wheel of a black Citroen C2 which was suspected of being stolen.
With Williams showing no sign of stopping for police, he was tracked on road by officers and in the sky with assistance from the National Police Air Service (NPAS) helicopter.