Jenkins married Pearl Decker in 1903; following her death he married Evelyn Thorstenberg on 1 December 1915. He was the father of three children: Mrs. Elliott (Edna) Anderson, the daughter of Pearl Decker; and Marvin Edward Jenkins and Mrs. Heber J. (Ruth) Player, born to Evelyn Thorstenberg.
Ab Jenkins acquired his first car in 1906 and began racing competitively in the 1920s. In 1926 he drove across the country from New York City to San Francisco in the time of 86 hours, 20 minutes. Two years later he completed his first twenty-four-hour race on a board track in Atlantic City, New Jersey. He went on to set numerous speed and endurance records on Utah's Bonneville Salt Flats and, in addition to building his own worldwide reputation, attracted other notable drivers to Utah, including England's Sir Malcolm Campbell, Captain E.T. Eyston, and John Cobb, who established land speed records of the measured mile on the Bonneville Salt Flats in the later 1930s. On Labor Day, 1950, Jenkins shattered twenty-six world and American records on the salt flats in his Mormon Meteor III. He attained a top speed of 199.19 miles an hour on a twelve-mile circular track. He established world records of 184.46 miles an hour for 100 miles; 190.92 for 200 miles; and 190.68 miles an hour for one hour of continuous running.
An active member of the Church of Jesus Christ of Latter-day Saints, he named his race cars "Mormon Meteor," giving credit to living the Mormon Word of Wisdom--abstinence from tobacco, alcohol, and coffee--for his endurance and athletic ability. For many years the "Mormon Meteor III" was on display at the Utah State Capitol Building. Beginning in 1991, a restoration of the car was undertaken by Ab's son, Marvin Jenkins. The race car was returned to the state capitol and a bronze bust of Ab Jenkins added to the exhibit on 21 October 1993.
Jenkins served as mayor of Salt Lake City from 1940 through 1943. He died 9 August 1956 in Wisconsin, where he had gone to drive the pace car for the Road American Auto Races in Elkhart Lake. Following funeral services in the Assembly Hall on Salt Lake City's Temple Square, Jenkins was buried in Wasatch Lawn Memorial Park on 13 August 1956.