The Pickel web site lists Jacob Bodine's parents as Jacob and Catherine Bodine. No source was given.
In the baptism records of St. James Lutheran ("Straw") Church in Greenwich, Warren Co., NJ there is a baptism for Balthazar and Anna Barbara. It is in 1770 and says this:
Balthaser Buckel [Biickel] and wife Anna Barbara--(child) b. July 8, bapt. Aug. 12--Sponsors Balthaser Bickel and wife Anna Barbara.
The record above only says "child." I don't know if it was Mary or Nicholas, but I would guess Nicholas. I think he was younger than his sister, Mary. I would think that Mary was born before 1770.