Bikeshare Transit Act of 2019 This bill allows bikeshare projects to be eligible for federal funding. Specifically, the bill makes a bikeshare project eligible to be an associated transit improvement project, including projects that (1) facilitate a bicycle rental operation that makes bicycles available for public transportation, (2) allow riders to pick up and drop off bicycles, (3) serve a defined geographic area, and (4) facilitate the transit of individuals between various points in the area. Public transportation capital projects must include any project for the acquisition or replacement of bicycles and related equipment, including technology and vehicles needed to restock stations, and the construction of bicycle-related facilities to facilitate a bikeshare project. The bill also makes bikeshare projects eligible for funds if they shift traffic demand to non-peak hours or other transportation modes, increase vehicle occupancy rates, or otherwise reduce demand for roads.