Expanding Private Airport Security Screening Act This bill makes various changes to a program that permits private companies to screen passengers and property at airports. Current law requires airport operators to submit an application to the Transportation Security Administration (TSA) in order to use a qualified private screening company. Additionally, under current law, the TSA (rather than airport operators) must enter into the contracts for screening services with such companies. Under this bill, the TSA must maintain a publicly available list of qualified private screening companies, and airport operators may directly enter into contracts for screening services with any company on the list. The bill also requires reporting related to the screening program. The TSA must annually report to Congress about the relative performance and costs of screening services carried out by private companies versus by federal government personnel. Additionally, the TSA must provide on a quarterly basis a comparison of the cost of providing services using the private company versus federal government personnel to airports that contract with private screening companies.