Trust in Public Service Act This bill incorporates customer experience as a central measure of performance for federal agencies. Specifically, the bill requires each agency to develop a high-quality customer experience by allocating sufficient resources to and prioritizing customer experience capabilities and initiatives, adapting government-wide and global good practices, streamlining the process for soliciting voluntary customer feedback and requiring limited internal review if the collection is within the scope of Office of Management and Budget (OMB) guidance, and using human-centered design practices. Each agency shall develop and use tools to experiment with different approaches to improve customer experience, ensure the privacy of federal customers, use the data collected to continually improve customer experience and agency performance, and share the data collected with research entities to permit external analysis. The bill sets forth agency communication responsibilities. In addition, the OMB must issue guidance for agencies in collaboration with specified entities. It may establish programs that annually recognize individuals and teams across the federal workforce meeting customer service-related goals. The bill (1) integrates customer experience provisions into the U.S. code and the Federal Citizen Services Fund, (2) directs the OMB to establish an Office of Customer Experience, and (3) integrates customer experience into the responsibilities of key agency officials. The OMB, in coordination with the Office of Customer Experience, must establish the Participatory Government and Civic Dialogue Advisory Council. The Government Accountability Office shall report to Congress, assessing agency efforts and examining best practices.