Apperson's debut came in 1949, when he competed at Hillsboro. Starting positions in all of his races that year are unknown, but Apperson had a nice effort that left him 13th. In fact, Apperson ran well in two other starts that year, finishing 15th at Hamburg and a career-best 11th place at North Wilkesboro. His 43rd in points was his best career showing as well.
Apperson stepped it up to a seven-race schedule to the 1950 season, again recording some respectable results. He finished in the top-thirteen three times, matching his career-best finish with an 11th place run at Langhorne. But Apperson also began to struggle with DNFs, finishing 25th or worse in the other four starts. This included a 61st place run at Darlington in the inaugural event there.
Apperson's final career race came in 1952, when he returned to Daytona Beach. Starting positions in the field of sixty-one are unknown, but Apperson had a so-so day in route to finishing 36th.