As had three previous generations of his family, Woodrum practiced law in Roanoke, Virginia. He was also active in various bar associations, the Roanoke Chamber of Commerce and the United Way. Woodrum also served on the board of directors of the Legal Aid Society of Roanoke from 1967 until 1976 and had also served as the organization's vice-president. His political career began in the Roanoke City Young Democrat Club in 1960, as the city bucked Massive Resistance advocated by the Byrd Organization. First elected to the Virginia House of Delegates in 1979, Woodrum served from 1980 until 2003. He served on the State Crime Commission beginning in 1982 and became its chair. He also served on the State Water Commission beginning in 1981. In the General Assembly, Delegate Woodrum served on the Courts of Justice committee and the Appropriations and Corporations, Banking and Insurance committees, among others. He modernized Virginia's Freedom of Information Act in the 1990s, and also helped construct programs to rehabilitate offenders, as well as to enable low income Virginians to attend college. Woodrum initially served alongside fellow DemocratVic Thomas. In 1979 they handily defeated Republicans Elizabeth T. Bowles and Mary Brooks, and in 1981 they significantly defeated Independent Zaman K. McManaway. His district, which comprised parts of the City of Roanoke as well as the County of Roanoke, was initially numbered the 7th Virginia district, but briefly became the 6th district in 1982. Further redistricting required by a judicial decision mandating single member districts again combined parts of the city and county, and renumbered it as the 16th district from 1983 until 2001. He often faced no opponent when re-elected, but soundly defeated Republican Newell R. Falkinburg in 1995 and Independent A.R. Sadjadi in 1999. After the Republican party took control of the House of Delegates in 2000, he lost his seat on the Appropriations committee and was redistricted into the same district as his ally, former majority leader Richard Cranwell. During his last term, until Woodrum declined to seek re-election, the district was numbered the 11th. After winning a primary contest against B.M. Shepard, lawyer Onzlee Ware succeeded him as that Roanoke district's delegate. The erudite and witty Woodrum then was appointed to the board of trustees of the Library of Virginia, where he served beginning in 2004 and as chair in 2011 and 2012.
Death and legacy
Woodrum died in Florida, where he normally spent winters.