Bob was born in Minneapolis and was adopted when he was four days old by Josephine and Lee Greg. They moved to McAllen Texas when he was nine years old and then to Camas, WA when Bob was fifteen. He graduated from Camas High School and attended Monmouth Teachers College in Monmouth OR.
His first race was driving a midget in 1938 at the Portland Speedway in Portland, Oregon. The following year in a B-Class midget and won the Oregon Midget Racing Associations B-Class championship.
He moved into the A-Class in 1940, finishing 12th in the points. This was the lowest he ever finished in any championship.
1941 was slightly better finishing tenth in the OMRA and the Northwest Association Championsips. It was also the year that he rolled for the first of seven times. In the days before roll bars he rode his luck at the Jantzen Beach Arena in 1941, 1945 and 1951 and in 1947 he rolled at Grants Pass, Oregon. In 1956 he rolled twice.
His worst crash came at Indy in 1950. After passing his driving test he was on his time trial run when, on the backstretch, a tie rod broke. Out of control he slid for 750 feet, hitting turn 3 guardrail, flipping over and then slid another 350 feet. His only comment, "I didn't make the race!"
Gregg won twenty-two championships in midgets or sprint cars in twenty-six years. This is believed to be the most any one driver has ever won in the history of auto racing in the Northwest. From 1958 up to and including 1962, Gregg won a thirteen championships in midgets including the Oregon, Washington and Northwest championships.
In 1964 with Canadian Modified Racing Association, Bob came third in points, and, at 44, was the oldest man racing on the CAMRA circuit. He was known as 'Bullet Bob the Barefoot Boy', because of his penchant for driving barefoot. In 2000 he was chosen as 'Driver of the Century' by Golden Wheels.