Most recently, Bjornestad was minister counsellor and deputy head of mission (2017 – 19) at the Norwegian embassy in Pretoria, South Africa, and deputy head of mission (2006 – 08, 2009 – 11) at the Norwegian embassy in Riyadh, Saudi Arabia. He also served as second secretary at the mission of Norway to the EU in Brussels (2001 – 04). He was an advisor to the Swiss Executive Director of the African Development Bank in Tunis in 2008-9. He served as a city councillor in Bergen and as an alternate member of the Norwegian parliament between 1989 and 1993. He attended the University of Mannheim, Germany; the University of Oslo, Norway; and Columbia University, New York, where he took a Masters in international affairs, economic policy management.