After college, he decided to give a music career a try and started singing professionally, dropping his first and last name to appear as simply "Oliver". His first success came when he recorded a song called "Good Mornin' Starshine", from the 1968 rock musical "Hair". Thanks in part to the exposure and controversy of the play, the song climbed to number 3 on Billboard's Hot 100 and became one of the best selling records of that year. The Brady Bunch, Strawberry Alarm Clark and Sarah Brightman, among others, also recorded versions of "Good Morning Starshine."
Following the same formula, Oliver's follow-up was a Rod McKuen tune that was featured in the 1969 movie, "The Prime Of Miss Jean Brodie" called "Jean". The soft ballad received lots of air-play and went to number 2 in the U.S.A.
The following year, he scored another Top 40 hit with "Sunday Mornin'", before teaming up with '60s hitmaker, Lesley Gore for a remake of the Fleetwood's "Come Softly To Me". The record, credited to "Billy and Sue" went nowhere and Oliver quickly disappeared from the charts. Resuming the name Bill Swofford, he toured hundreds of college campuses in the eastern and southern United States in 1976 and 1977, but a short-lived teaming with Karen Carpenter during the same period proved unsuccessful. He kept busy singing small parts on Broadway for a brief period before leaving the music business in the early 1980's.
Oliver's name came into the public eye again in the '90s when he became one of the few artists, along with Paul Anka and the Captain and Tennille, to have more than one song named among The Worst 100 Singles of the Last 25 Years, by David Browne and David Hinckley for The New York Daily News. Both "Jean" and "Good Morning Starshine" made the list. This list however can't be taken too seriously, as such Rock legends as Mick Jagger and Michael Jackson ("State of Shock"), Paul McCartney ("Silly Love Songs" and "Ebony & Ivory") and Stevie Wonder ("I Just Called to Say I Love You" and "Ebony & Ivory") also made the list. Someone once said that "a critic writing about music is like a man with no legs writing about shoes".
Oliver died of cancer at the age of 54, on Saturday, February 13th, 2000 in Shreveport, Louisiana. On June 4th, 2009, a resolution was introduced in the North Carolina General Assembly honoring the late singer.