Bosley is best known for portraying Howard Cunningham on the ABC sitcom Happy Days (1974–1984) for which he received a Primetime Emmy Award for Outstanding Supporting Actor in a Comedy Series nomination.

He's also known for his film appearances in Love with the Proper Stranger (1963), The World of Henry Orient (1964), Divorce American Style (1967), Yours, Mine and Ours, The Secret War of Harry Frigg (both 1968), Gus (1976), and The Back-up Plan (2010).

He gained attention as a character actor performing various roles in shows such as Naked City, Profiles in Courage, The Defenders, Night Gallery, Get Smart, Bewitched, and Mission: Impossible.

[3][4] Bosley played the Knave of Hearts in a Hallmark Hall of Fame telecast of Eva Le Gallienne's production of Alice in Wonderland in 1955.

In 1962, he portrayed Assistant District Attorney Ryan in the episode "The Man Who Wanted to Die" on James Whitmore's ABC legal drama The Law and Mr. Jones.

[6] He also appeared on episodes of Bonanza, Bewitched, Get Smart, The Silent Force, The Streets of San Francisco, Night Gallery, A Touch of Grace, and The Love Boat.

Other films include The World of Henry Orient; Divorce American Style; Yours, Mine and Ours; Gus and the made-for-television The Triangle Factory Fire Scandal.

Among myriad television appearances, one notable early performance was in the "Eyes" segment of the 1969 pilot of Rod Serling's Night Gallery, directed by Steven Spielberg and starring Joan Crawford.

His film appearances included roles in Love with the Proper Stranger (1963), The World of Henry Orient (1964), Divorce American Style (1967), Bang Bang Kid (1967), The Secret War of Harry Frigg (1968), Yours, Mine and Ours (1968), To Find a Man (1972), Mixed Company (1974), The Night That Panicked America (1975), Gus (1976), The Triangle Factory Fire Scandal (1979), O'Hara's Wife (1982), Million Dollar Mystery (1987), and Wicked Stepmother (1989).

He provided the voice of the title character in the 1980s cartoon The World of David the Gnome and the shop owner Mr. Winkle in the children's Christmas special The Tangerine Bear.

[12] On April 19, 2011, Bosley's estate and four of his Happy Days co-stars, Erin Moran, Don Most, Marion Ross, and Anson Williams, filed a $10 million breach-of-contract lawsuit against CBS, which owns the show, claiming they had not been paid for merchandising revenues owed under their contracts.