Hastings started in radio on "Coast-to-Coast on a Bus" (NBC). Hastings served during World War II in the United States Army Air Corps. After serving in World War II as a navigator on B-29s, he played the role of Archie Andrews in a series based on the Archie comic book series on NBC Radio from 1945-53. Archie Andrews was sponsored by Swift & Company food products.

Hastings moved to television in 1949, performing in early science-fiction series, including Atom Squad. In 1954, he was the featured pitch-man (acting as an amateur magician) for Bakers Instant Cocoa Mix television commercials. His first recurring role was as a lieutenant on Phil Silvers' Sergeant Bilko series in the late 1950s. At that time he also guest-starred on Walter Brennan's ABC sitcom The Real McCoys, in an episode titled “How to Paint a House”. He appeared as well in a few episodes of Captain Video playing the brother of "The Video Ranger", who was in turn played by Hastings' brother, Don Hastings.

Hastings has also done voice work for animation and commercials, including Beany on Beany and Cecil, The Raven on the Munsters series, Superboy in The New Adventures of Superboy cartoons of the 1960s, D.D. on Hanna-Barbera's Clue Club, and the voice of Commissioner Jim Gordon in the popular Batman: The Animated Series and its various spinoffs in the DC animated universe, such as Batman: Mask of the Phantasm, Superman: The Animated Series, The New Batman Adventures and several Batman video games.

Hastings in 1962 played a railroad executive in the episode "Substitute Sheriff" of the NBC western series The Tall Man.

He appeared five times on CBS's Dennis the Menace, with Jay North, most notably as Coach Gilmore in the 1963 episode "The Big Basketball Game". He appeared three times from 1961 to 1962 on the CBS sitcom Pete and Gladys, with Harry Morgan and Cara Williams.

In 1967, Hastings recorded an LP for Home Records Incorporated, one titled Bob Hastings Sings For The Family (HR-101), with 12 songs arranged and conducted by Bob Caudana.

Hastings was in the 1968 Universal film Did You Hear the One About the Traveling Saleslady? starring Bob Denver, as well as The Bamboo Saucer (1968), Angel in My Pocket (1969), The Love God? (1969) starring Don Knotts, and The Boatniks (1970). In 1971 Hastings was cast in the comedy movie How to Frame a Figg, also starring Don Knotts, and also had roles in The Poseidon Adventure (1972), The All-American Boy (1973) and No Deposit, No Return (1976). Hastings also was in the 1978 movie Harper Valley PTA in which he played Skeeter Duggan, a member of the PTA board who had been kidnapped at the orders of its dishonest President to commit election fraud, and played "Cousin Phantom of the Opera" in the 1981 television movie The Munsters' Revenge.

His earlier work in animation includes doing the voice Henry Glopp on Hanna-Barbera's animated series Jeannie in 1973 and additional voices on Challenge of the Superfriends.

Hastings was the older brother of longtime As the World Turns star Don Hastings. He was married to Joan (Rice) Hastings for 66 years and has four children, 10 grandchildren, and twelve great-grandchildren. He toured the country as a participant in various Old-Time Radio Conventions, reading scripts for such shows as Archie Andrews and The Bickersons. He appeared at the 2013 Cincinnati Nostalgia Expo, the Radio Enthusiasts of Puget Sound Showcase 2013 in Bellevue, Washington, in June, and at the Friends of Old Time Radio Convention in Newark, New Jersey, in October 2010.

He died on June 30, 2014, from prostate cancer at age 89. His funeral Mass was held in Burbank, California's Saint Finbar Catholic Church.