Bob Veith was born in Tulare, California and began racing in 1948 driving roadsters as a member of the California Roadsters Association.
Veith drove in 54 National Championship races between 1955 and 1968 and had a reputation for being able to qualify for a race with very little practice time. He also had a high degree of mechanical empathy and of his 42 starts between 1955 and 1960, 29 resulted in top-10 finishes, and twelve of those were in the top six.
Of his 11 starts in the Indianapolis "500," six ended up in the top 12. His best finish at Indy, was 7th at his first attempt in 1956, earning him Rookie of the Year honors.
Veith's best chance of a win at Indianapolis came in 1958. But, having qualified in 4th spot, he got tangled up in the first-lap accident that sadly took the life of Pat O'Connor.
In June that year Veith was one of the Americans chosen to drive in the "Race of Two Worlds," a three part 500-mile race at Monza, Italy. The fastest of the Americans in qualifying, he finished third to Jim Rathmann and Jimmy Bryan in the first leg and then runner-up to Rathmann in the second. The in August, he finished second to Rathmann in the Milwaukee 200.
In the 1964 "500," Veith drove a rear-engine car that A. J. Foyt had tested and turned down. He was running in third spot when he retired.
Veith also competed in USAC sprint car races, ranking fourth in the 1956 Midwest point standings. Between 1955 and 1957, he had eight feature finishes of either second or third.
He was a member of the Champion Spark Plug Company's Highway Safety program in which Indianapolis 500 drivers would visit high schools to talk to students about safe driving.
Veith was inducted into the BCRA and the Indy "500" Hall of Fame.
He retired from racing in 1969 to his ranch in Hales Grove. He was active in the Westport Volunteer Fire Department and was Landlord of the Hollow Tree Creek Salmon Hatchery as well as on the Board of the Salmon Restoration Association, who work to restore the natural wild salmon runs in the rivers of Northern California. After his home burned down, he moved to Santa Rosa, where he died in 2006, aged 81.