The train in the photo likely terminated at Bedford Park Blv'd on the Jerome Ave #4 line. This station has always been a connection to Westchester bound buses. Circa 1970, the bus companies servicing this station included Club Transporation and Westchester Street Transporation. Both companies offered special bus service to Yonkers Raceway and very likely supplied connecting service from Bedford Park to the Raceway.
In fact, I recall several times seeing Club Trans buses signed up for Yonkers Raceway and as mentioned above, I believe these coordinated service with the subway.