Go to U.S. Bureau of Labor Statistics - Collective Bargaining and Union Membership.

Go to Statistical Abstract of the United States (2013 to present) and navigate to the Labor Force, Employment, and Earnings section. For pre-2013 Statistical Abstracts, refer to the U.S. Census Bureau's Statistical Abstracts Series. 

The Union Membership and Coverage Database, constructed and maintained by Barry Hirsch (Georgia State University), David Macpherson (Trinity University), and William Even (Miami University) includes public and private sector labor union membership, coverage, and density estimates compiled from the monthly Current Population Survey using Bureau of Labor Statistics methods. 

See the US Department of Labor - Office of Labor-Management Standards (OLMS) for private and public sector agreements.