Hubbard was born in Murray, Kentucky, attended public schools, and graduated from Louisville Eastern High School in Middletown, Kentucky in 1955. Hubbard graduated from Georgetown College in 1959 and from the University of Louisville law school in 1962.

Hubbard began a law practice in 1962 in Mayfield, Kentucky. He was elected to the Kentucky Senate and served there from 1968 to 1975.

In 1974 Hubbard ran against the incumbent Democrat Frank Stubblefield in the Democratic primary for Kentucky's first district seat on the United States House of Representatives. The 1st District was (and is) in the far western part of the state. Hubbard upset Stubblefield in the primary and went on to win the seat. Hubbard was president of the House freshman class of 1974. He was re-elected to the House seat in 1976 and 1978.

In 1979 Hubbard ran for Governor of Kentucky but lost in the Democratic primary to John Y. Brown, Jr. Hubbard won 68,577 votes in the primary, finishing fourth behind Brown, Terry McBrayer and Louisville mayor Harvey I. Sloane, but ahead of Thelma Stovall, who was Lieutenant Governor of Kentucky at the time.

Hubbard was re-elected to the House in 1980 and five more times after that. While serving his ninth term, Hubbard was defeated for re-election in the Democratic primary by Thomas Barlow.

Hubbard came to the attention of investigators as the Rubbergate House Banking Scandal erupted. Hubbard was eventually indicted on counts related to his misuse of government property and personnel for his own political purposes and benefit. Hubbard's wife was also caught up in his criminal conduct; she had unsuccessfully sought Kentucky's 5th District congressional seat in 1992 as Hubbard unsuccessfully sought re-election to the House.

Hubbard sought to mitigate his criminal penalty by acting as an informant for the FBI under the code name "Elmer Fudd" but federal officals said that Hubbard was unreliable and only provided useless information. Hubbard then drew national attention by going public in 1993 about his 'informant' role and complained to the media about his situation. Federal officials responded that Hubbard blew his cover when he gave interviews to the Washington Post and network news shows about his 'informant' role.

In 1994 Hubbard pleaded guilty to three felony charges and received a sentence of three years in federal prison and a fine of $153,000. He was convicted of charges related to his violation of federal campaign spending rules, theft, conversion of federal property (using his congressional staff to help his wife's unsuccessful race for Congress in 1992), and obstruction of justice by trying to conceal records during the investigation. The last charge included staging a burglary at his Paducah office and reporting that certain records were stolen.

Hubbard's wife was also convicted of a crime, a misdemeanor, for her role in Hubbard's fraudulent activities on her behalf.

Hubbard was one of a handful of members of the House freshman class of 1974 to become a convicted criminal. Rep. Fred Richmond of New York was charged with tax evasion and possession of marijuana and resigned his seat as part of a plea bargain in 1982. John Jenrette of South Carolina was convicted in the Abscam bribery scandal, and as a result resigned in 1980 and went to prison.

In 2002 after Hubbard had been released from prison the Kentucky Supreme Court controversially reinstated Hubbard's law license in spite of his felony conviction. The Court did this despite a unanimous 16-0 vote by the Kentucky Bar Association against giving Hubbard back his law license. At the time, Hubbard said he was $411,000 in debt.

In 2005, Hubbard announced he was seeking a political comeback by running for election to the Kentucky Senate from a district centered on Paducah, Kentucky.