He is best remembered for his longtime recurring role as well-spoken, wisecracking Dr. Gamble on the radio comedy Fibber McGee and Molly and for voicing the Warner Bros. cartoon character Elmer Fudd.

[11] In 1938–1940, he was a regular on The Grouch Club, which aired on the CBS Pacific network[12][6] and was featured in some short-subject films made by the group.

Although his first forays into that medium were accompanied by instructions that he use the Fudd voice, Bryan soon came to the attention of Don Quinn and Phil Leslie, the production and writing team responsible for Fibber McGee and Molly and their supporting characters, two of whom spun off into their radio hits, The Great Gildersleeve and Beulah.

The Gildersleeve character, played by Harold Peary, became series broadcasting's first successful spin-off hit; that plus the onset of World War II (which cost Fibber McGee & Molly their Mayor La Trivia, when Gale Gordon went into the Coast Guard in early 1942, and "The Old Timer" Bill Thompson was drafted almost a year later) nabbed nearly every other remaining male voice.

[16] On May 5th 1949, Bryan appeared as "Clarence, the Guardian Angel" on the Screen Directors Playhouse radio series' rendition of Frank Capra's film It's a Wonderful Life.

Bryan's final original work as Fudd came in the Warner Bros. Edward R. Murrow spoof Person to Bunny.

On The Halls of Ivy, Bryan played Professor Warren, head of the college's history department, a role he also had on the radio program of the same name.

[5] On September 17, 1956, he became ill with acute gastritis while rehearsing for an episode for Producers' Showcase called "The Lord Don't Play Favorites", three hours before its airtime.