Bridge Quality Preservation Act This bill establishes certain requirements to address corrosion control in bridge and railroad-bridge projects that receive federal assistance. Specifically, certified contractors must employ a substantial number of individuals who are certified by a qualified training program in corrosion control, mitigation, and prevention in order to work on certain aspects of bridge project activities. A certified contractor must also provide training for any non-certified coating applicators employed by the contractor to work on a project. The bill further requires bridge projects to implement a corrosion management system that utilizes industry-recognized standards and corrosion mitigation and prevention methods for construction, repair, and maintenance projects. In addition, the bill expands the scope of the Railroad Rehabilitation and Improvement Financing Program to include corrosion control work on rail bridges. (This program provides direct loans and loan guarantees for the development of railroad infrastructure.) The bill also requires the Department of Transportation to study best practices for inspecting and addressing corrosion on weathering steel bridges. This report must be made available to state and local governments, metropolitan planning organizations, and regional organizations.