A Los Angeles, California native, Washburn's first uncredited role was as 6-year-old Walda Kowalski in the 1950 film about a smallpox outbreak in New York City entitled, The Killer That Stalked New York. She appeared on many of the anthology series then Common on American television networks, including The Ford Television Theatre, Lux Video Theatre, Jane Wyman's Fireside Theatre, Chevron Hall of Stars, H. J. Heinz Company's Studio 57, Four Star Playhouse, Dick Powell's Zane Grey Theater, Schlitz Playhouse of Stars, The 20th Century Fox Hour, Alcoa Presents: One Step Beyond, Shirley Temple's Storybook, and General Electric Theater, hosted by Ronald W. Reagan.

In 1951, Washburn appeared in the theatrical film Superman and the Mole Men, which was thereafter edited into two half-hour segments. These became the first two episodes of the television series The Adventures of Superman, starring George Reeves and Phyllis Coates. In 1951 she also appeared as an orphaned French girl in Frank Capra's film, Here Comes the Groom, starring Bing Crosby, Franchot Tone, Alexis Smith,and Jane Wyman. In 1955, Washburn appeared as a daughter of Stephen Dunne and Barbara Billingsley in the nearly forgotten CBS sitcom Professional Father. Phyllis Coates appeared in that same series too as a nurse, Madge Allen. George Reeves also appeared with Washburn in one of her Ford Theatre episodes.

She also appeared in episodes of the Warner Bros. ABC detective series, 77 Sunset Strip and Hawaiian Eye. She appeared twice on the CBS western series, The Texan starring Rory Calhoun, as Henrietta Tovers in "No Tears for the Dead" (1958) and as Greta Banden in "Badman" (1960). She appeared in the debut episode of NBC's Wagon Train but not in the lead role. Her episodes included the episodes "The Willy Moran Story" (1957), "The Tobias Jones Story" (1958), and as Milly Sharp "The Cassie Vance Story" (1963). In "Tobias Jones", her co-star was Comedian Lou Costello, in his first dramatic role. Washburn's other roles included two appearances each on Arrest and Trial, Mr. Novak, and Gidget and single guest-starring roles on The Patty Duke Show.

She was cast as a young girl in the Leave It to Beaver episode entitled "Blind Date Committee" in October 1959, on NBC's The Loretta Young Show, and as an older teenager in Loretta Young's 1962–1963 CBS family drama, The New Loretta Young Show. In between, Washburn played Lili Kilgore in the 1956 film The Lone Ranger, and Lisbeth Searcy in the 1957 Walt Disney film Old Yeller, the story of a beloved dog, starring Fess Parker, Dorothy McGuire, Tommy Kirk, Kevin Corcoran, and Jeff York in the role of Lisbeth's father, Bud Searcy. Washburn appeared once on NBC's Star Trek in the role of Lieutenant Arlene Galway in the 1967 episode "The Deadly Years".

Later, young Washburn appeared on Leave It to Beaver, a popular sitcom in which Billingsley played the mother, June Cleaver. Washburn's other roles included Jack Webb's Dragnet, The Lone Ranger, Fury, The Millionaire, The Law and Mr. Jones, and Target: The Corruptors!, a series about crusading journalists starring Stephen McNally and Robert Harland. She also portrayed the character Lolly Harrod in the 1961 episode "Parasite Mansion" of Boris Karloff's NBC suspense series, Thriller Washburn appeared on radio with popular Comedian Jack Benny even before she guest starred on CBS's The Jack Benny Program on television.

She appeared in several episodes of Gidget from 1965-1966 under various names. This included playing the daughter of Paul Lynde in the episode, "Take a Lesson".

In the 1970s, she appeared in three episodes of Quinn Martin's The Streets of San Francisco crime drama with Karl Malden': "Most Feared in the Jungle" (1973), "Letters from the Grave" (1975), and as Michelle Rhodes in "Let's Pretend We're Strangers" (1977). One of her later television appearances was in the 1984 episode "Remembrance of Things Past" of CBS's Scarecrow and Mrs. King. Her most recent role was that of the character Brenda in the 2007 film Hard Four, which also features Ed Asner, Paula Prentiss, Dabney Coleman, and Ed Begley, Jr. In 2015, she appeared as Reyna Belasco Rosenthal in R. Christian Anderson's feature film When the World Came to San Francisco.

Washburn is an aunt of Actress Darlene Tompkins, who is only three years her junior. Her brother, George Washburn, who died of a heart attack in 1994, was an actor, stuntman, and race car driver.