In the early 1940s, Bexley started doing stand-up comedy in upstate New York. He worked with Milton Berle, Danny Kaye, and Henny Youngman, and danced with Sammy Davis Jr..

When Bexley returned from Europe in 1969, he and Foxx were cast together in Cotton Comes to Harlem (1970). Upon Bexley's arrival from Asia in 1971, Foxx sent for him to join in the NBC sitcom Sanford and Son. It was Foxx who convinced Bud Yorkin and Aaron Ruben to hire Bexley to play one of Fred G. Sanford's friends. At the time, Bexley was 62 years old and had never appeared on television before. Bexley gained international popularity for his portrayal as "Bubba" on the series, which is a very successful "rerun sitcom" even today.

Sanford and Son, based on a British show Steptoe and Son, was an instant hit and remained in the country's top 10 programs for its entire run from 1972 to 1977. Bexley reprised Bubba in the short-lived sequel, Sanford Arms, which had many of the same characters but not Foxx and Demond Wilson.

He appeared in many television shows such as Cheers, Hunter and Laverne & Shirley, as well as the 1976 film Sparkle. One of his final appearances on television was in an episode of Foxx's The Royal Family. In the episode, "New Beginnings", Bexley made a special guest appearance as an old friend of Al Royal's (Foxx) who attends his funeral.

Bexley was born in either Jamestown, Virginia or Detroit, Michigan to the late Mr. and Mrs. Thomas Bexley. His father was a Bible scholar and Teacher and his mother a classical vocalist. "I was born with a flair for the stage, as I had always been a clown - even during early adolescence," Bexley wrote in 1983.

In 1989, Bexley was awarded the "Outstanding Senior Citizen of the Year" award by the Support the Artists of America (STAA) in Orlando, Florida.

Since his relocation to Hampton, Virginia (before that, he resided in the San Fernando Valley) during the 1990s, Bexley was still quite active, always working on new ideas for shows and live performances.

Bexley had a close friendship with Redd Foxx, until Foxx's death in October 1991. He attended Foxx's funeral in Las Vegas, where he was an honorary pallbearer. Their friendship lasted for nearly fifty years.

Bexley made personal appearances and signed autographs on many occasions, including the Newmarket Fair Day-Talent Show on September 1996, and the Aberdeen Athletic Association on June 1996. One of Bexley's last signings was during his attendance at the NASA Langley Research Center's "Black History Program," on February 1997. These types of activities added to his longevity.

Bexley died of heart and kidney failure on April 15, 1997, at Hampton Sentara Hospital, in Hampton, Virginia. He was 87 years old. He is survived by his wife Sally Bexley and his two daughters Donna and Stacies Marie, as well as grandchildren, great-grandchildren, nieces and nephews.