Hume appeared in the series in 1964, completing two races late in the year. In his debut at Darlington, Hume started 28th but slid to 38th after an early crash. Hume would then barely improve at Charlotte, where Hume finished 35th due to overheating.
Hume had a signifcantly better season in 1965, when he competed in four events. Hume only managed to finish one of the four races. That race, which came at Charlotte, Hume finished 18th. The good news for Hume were that all of his DNFs were due to mechanical issues.
Hume returned to the series after a sixteen-year absense in 1981, completing one race for D.K. Ulrich. He started the race at Rockingham in 33rd position and would finish there after an early race crash.
Another multiple year absense ended in 1984, when Hume ran a race for Bahari Racing. After starting 23rd at Atlanta, Hume came home with a 26th place finish. He would finish that event twenty-nine laps down.
Hume ended his career with a seven-race swan song in 1985. It was a decent season, driving for James Hylton. In his seven starts, he once again struggled to finish races, only completing four of those. However, all four ended up being top-21 finishes. The best of the year, and as a result his career, was a 16th place effort at Bristol. After a 38th place showing in points, Hume was replaced and he has not driven in NASCAR since and likely won't due to his age.