In his early days, Bob, who changed the spelling of his last name because the announcer of the Milton Berle radio show kept mispronouncing it, gained prominence by winning the ''Allen Amateur Hour'' on Fred Allen's radio show. He began his professional career singing in clubs around his hometown of Hoosick Falls, in upstate New York, where the Dorsey Brothers discovered him and later hired him to replaced the departing Bob Crosby.
Eberly started work in the spring of 1935, just before Tommy walked out on the orchestra. He stayed with Jimmy for eight years and became one of the top male vocalists of his day, rivaling Bing Crosby and later Frank Sinatra for that title. Well-liked by his peers, he became best friends and eventually roommates with Jimmy Dorsey. Throughout his career he was encouraged by many in the industry to strike out on his own, but he refused. He was perfectly happy earning a weekly salary with Dorsey's group. Most famous are his duets with Helen O'Connell, in whom he also had romantic interest.
In December of 1943 his relationship with Dorsey finally ended when he entered the army and was stationed in the Chicago area with Wayne King's orchestra. His two years in the service severely hurt his career. After he received his discharge he returned to the civilian music world to find he had been largely forgotten by the general public. Nevertheless, he remained active in the music industry for the rest of his life, singing mainly in small clubs. During the early 1950s he was a regular on the television program TV's Top Tunes. In 1980 he had one lung removed but still continued to sing. He died of a heart attack in 1981.