Buster was signed by the Orioles in 1958, and spent 6 seasons in their farm system, mostly as a starting pitcher. Although he appeared in 7 games for the Orioles in 1963, he was traded to the Senators in March 1964 for a player to be named later (Lou Piniella).
Narum spent 2 full seasons with the Senators in 1964-65 as a key member of their starting rotation. He appeared in 84 games over that span, but compiled records of 9-15 and 4-12 (in his defense, it WAS the Senators!).
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For whatever reason, his big-league career evaporated after that. He spent most of the next 2 seasons pitching for the Nats' triple-A team in Hawaii (hey, if you've gotta play in triple-A, that's the place to do it!), while making token appearances in Washington: 3 innings with a 21.60 ERA in 1966, and 2 games in 1967.
In February 1968, Buster was part of a 6-player trade with the White Sox, but spent the entire season at triple-A Buffalo (quite an adjustment from Hawaii). His final season was 1969, toiling with the Cardinals' AAA team in Tulsa, OK.