Actually Wednesdays, Bronx Zoo is only free by donations only. You could pay whatever you wish. Only rides and exhibits are not free.
Free Admission to the Bronx Zoo
Yes! Admission is free on Wednesdays. Parking is not on any day.
Also, if you are a minor, you can ALWAYS get fee entry into the Bronx Zoo.
However, an adult must be with you then and unfortunately, they will have to pay.
"Visitors under age 17 must be accompanied by a chaperone."