Bradley's debut came in 1962, when he managed to finish 59th in the points despite just competing in three races. It was little wonder as Bradley proved from the start that he had talent. He started 19th but quickly made his way to 7th by the end of the race at Richmond in his first start, quickly following that up with a career best start (8th) and finish (4th) at Moyock. After an 11th place run to conclude the year at Martinsville, Bradley had an average finish of 7.3 for the year - not too shabby for any young driver.
Bradley surprisingly did not return until 1967, when he ran his final three races. This season, however, proved to be more a struggle for the driver. He fell out of his first two races that year, struggling to 17th in the Richmond race and finishing 27th in his first trip to Beltsville. But Bradley salvaged the end to his career, closing out with a 10th place run at North Wilkesboro.