Apprenticeship Improvement Act of 1993 - Amends the National Apprenticeship Act to direct the Secretary of Labor to establish and maintain a national information collection system for apprenticeships and apprenticeship programs. Requires the Secretary to reserve at least one percent of appropriations under such Act to establish outreach recruitment activities to increase the participation of women and minorities, handicapped individuals, displaced workers, and disadvantaged individuals in the apprenticeship programs. Establishes the Bureau of Apprenticeship and Training (the Bureau) in the Department of Labor, under the direction of the Administrator of the Bureau of Apprenticeship and Training. Transfers to the Bureau all functions of the Assistant Secretary for Employment and Training Administration with respect to the promotion of labor standards of apprenticeship, including research, information, and publications. Transfers to the Bureau all functions related to apprenticeship, including appropriate administrative and program support services, together with necessary personnel and related funds. Directs the Secretary to increase the force within the Bureau to a specified number of full-time employees. Limits the authority to conduct reductions in force within the Bureau of Apprenticeship and Training. Directs the Secretary to report to the Congress within six months on whether the apprenticeship program complies with regulations governing equal opportunity.