Bibby was elected to the Scottish Parliament in 2011 to represent the West of Scotland region, as the Labour Party returned three members from the list. Born in Paisley, Neil grew up in Renfrewshire and went to the University of Glasgow. Bibby had been Chair of Young Labour United Kingdom and Chair of Scottish Labour Students.
In 2007 he was elected to Renfrewshire council in Johnstone North, Kilbarchan and Lochwinnoch ward.
Before becoming elected to the Scottish Parliament he worked for Jim Murphy Member of Parliament and Ken Macintosh Managing Successful Programmes. He is currently the Scottish Labour Chief Whip and is a substitute member on the Welfare Reform Committee, as well as Company-Convenor of the Cross Party Group on Rail and the Deputy Convenor of the Cross Party Group on Visual Impairment. Neil is standing for the Paisley seat in the Scottish Parliament election, 2016.