Russell was born Neil Oliver Russell in Brattleboro, Vermont, the son of Ruth Stewart (née Vogel) and Warren Oliver Russell. He always wanted to become an actor and studied drama at Brattleboro High School. As a boy, he was dubbed an unofficial mascot of the New York Yankees, becoming good friends with such players as Lefty Gomez and Joe DiMaggio. Also, Lou Gehrig, who was already weakened by illness, gave him the last bat he used to hit a home run before his retirement.
During part of the 1950s, Bing ran "Teddy's Restaurant" in Newport, New Hampshire, where a co-working waitress, Alfreda Couitt (Barney), introduced Bing to his future wife, Louise.
Russell made his debut in the film Cavalry Patrol, and had some uncredited roles in his early career.
Best known as Deputy Clem Foster on Bonanza (1959) and Robert in The Magnificent Seven (1960), he guest starred in episodes of many television series, including Playhouse 90, Highway Patrol, Wagon Train, The Life and Legend of Wyatt Earp, The Loretta Young Show, Johnny Ringo, Walt Disney's Wonderful World of Color, The Rifleman, Maverick, Zane Grey Theater, Route 66, Rawhide, Ben Casey, The Untouchables, Hazel, The Andy Griffith Show, The Twilight Zone, The Donna Reed Show, The Munsters, Combat!, Branded, The Fugitive, The Monkees, I Dream of Jeannie, Ironside,The Big Valley, Death Valley Days, Adam-12, The Virginian, Alias Smith and Jones, The Mod Squad, Mannix, The Rockford Files, The Streets of San Francisco, Emergency! and Little House on the Prairie.
In 1963, he was cast as John Quigley, a Chicago mobster, in the episode "Five Tickets to Hell" of Jack Webb's CBS anthology series, GE True. In the storyline, Quigley travels to Chihuahua, Mexico, where he robs the mint of $500,000 and kills seven men in the commission of the crime. Police Lieutenant Juan Garcia (Carlos Romero) tracks down Quigley and his three accomplices. BarBara Luna also appears in the episode.
In another 1963 appearance in the episode "The Measure of a Man" on the syndicated Western series Death Valley Days, Russell plays the outlaw Burt Alvord, who is promised a lenient sentence if he will surrender and reveal the location of the notorious bandit Augustine Chacon (Michael Pate). Rory Calhoun was cast as the Arizona Ranger Burt Mossman who convinces a reluctant Alvord to set a trap to catch Chacon. Mossman has Chacon handcuffed and orders Alvord to toss away the key. Chacon is hanged thereafter for a past conviction of which he had escaped.
Russell appeared in the original pilot (filmed in November 1965) for The Monkees TV series as Rudy, a record store owner and the group's manager; after the show was greenlit by NBC, the concept of a manager was discarded and Russell's character was not retained. An edited version of this pilot, in which Russell appears, was broadcast as a regular episode of the first season, and is part of the show's syndication package to this day.
Russell much later played Vernon Presley to his son Kurt's Elvis Presley in the television movie, Elvis (1979).
Russell owned the Portland Mavericks, the only independent team in the Class A Northwest League. Russell kept a 30-man roster because he believed that some of the players deserved to have one last season. His motto was fun. He created a park that kept all corporate sponsorship outside the gates, hired the first female general manager, Lanny Moss, in professional baseball, and named the first Asian American GM/Manager. His team set a record for the highest attendance in minor league history, but lost the 1977 pennant to the Bellingham Mariners. Subsequently, Major League Baseball regained interest in Portland and resurrected the Class AAA Portland Beavers minor league franchise. The Portland area was recovered but paid Russell the highest payout in history for a minor league territory after Russell took the matter to arbitration. Ex-major leaguers and never-weres who could not stop playing the game flocked to his June try-outs, which were always open to anyone who showed up. The team and archival footage of Russell were featured in the documentary The Battered Bastards of Baseball (2014).
Russell died from complications of cancer on April 8, 2003 in Thousand Oaks, California.