Myers was born in Harrison County, West Virginia, to parents John R. Myers and Flonnie Wade Myers. He became involved in racing in the late 1940s, initially serving as a mechanic for his younger brother Bobby, who had already established himself as a regular at Bowman Gray Stadium. Billy eventually transitioned from the garage to the cockpit.
Bowman Gray Stadium defined Myers's career. He won the modified track championship there three times — in 1951, 1953, and 1955 — and accumulated 22 Modified and Sportsman race victories at the quarter-mile oval over his career. This record earned him the enduring nickname "Mr. Bowman Gray," an identity that outlasted his presence in NASCAR's premier division.
Myers made his debut in the NASCAR Grand National Division in 1951, finishing eighth at Asheville-Weaverville Speedway. Early in that season he also drove for Hubert Westmoreland at Detroit and Darlington, placing 18th in the Southern 500. He raced the R. G. Shelton No. 22 Hudson at Martinsville Speedway, taking a third-place finish.
After stepping back from Grand National competition, Myers returned in 1955, this time competing primarily in the NASCAR Sportsman Division, where he won the national championship with 4,810 points — finishing more than 1,000 points clear of runner-up Ralph Earnhardt.
The 1956 season was his most productive in NASCAR's premier series. Racing in 42 of 56 scheduled events, he claimed his first Grand National victory at West Palm Beach on March 4, 1956. He added a second win at Norfolk Speedway on August 22 and finished sixth in the season's final points standings, with 13 top-five and 22 top-ten finishes. He also won his sole NASCAR career pole, at Soldier's Field, though brake failure relegated him to 17th in that race.
In 1957 Myers made 28 starts in the Grand National Division, collecting four top-fives and nine top-tens. He also competed in the NASCAR Convertible Series, winning at Wilson Speedway. His final Grand National starts came at Daytona and Concord in early 1958. He had returned to the Convertible Series that same year, winning at North Wilkesboro Speedway, just weeks before his death.
On April 12, 1958, while competing in a Modified race at Bowman Gray Stadium — the track he had long dominated — Myers suffered a heart attack at the wheel and crashed into the fence. He died that day. His brother Bobby had died on the same track, the Darlington Raceway, on September 2, 1957, during the Southern 500.
In honor of Billy and Bobby Myers, NASCAR annually presents the Myers Brothers Award to the individual, corporation, or entity judged to have made the greatest positive contribution to stock car racing that year. The award ensures the brothers' names remain woven into the fabric of the sport they helped build during its formative decade. Myers's son Gary later competed in the NASCAR Cup Series, and his grandchildren Burt and Jason raced on the Whelen Southern Modified Tour. His nephew Danny "Chocolate" Myers became a prominent NASCAR pit crew member, serving as gasman for Dale Earnhardt's Richard Childress Racing team.