Bikeshare Transit Act of 2017 This bill makes a bikeshare project eligible to be an associated transit improvement project, including one carried out to facilitate a bicycle rental operation that makes bicycles available for public transportation, allows riders to pick up and drop off bicycles, serves a defined geographic area, and facilitates the transit of individuals between various points in the area. Public transportation capital projects shall 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 eligible for funds under the congestion mitigation air quality improvement program projects or programs that reduce demand for roads through bikesharing.