He was married to Elizabeth Martino (daughter of Benjamin Martino) on October 23, 1814 in the Moravian Church on Staten Island.
He had children, but he had died by the time of his father's will. There is a John V. Bodine buried in Trinity Chapel Cemetery where his parents are buried. That is probably this John.
The following, which probably refers to this Johh, comes from "Vosburgh's Inscriptions, Church of the Ascension" (# 397) and was sent to me by Janet Britton:
In Memory of John V. Bodine, who departed this life August 11th 1821, Aged 32 years, 5 months & 9 days.
Whilst on earth I did remain
Afflicted sore with grief and pain
My cries and prayers where heard
I was oppressed with pain and grief
But Jesus granted kind relief
To all my sighs and tears.
He appears to be associated with Edward Bodine and Phoebe Bush. Bodine was listed on the same sheet at FamilySearch.com with John and Betsey's two children. I'm not absolutely sure that this John married Elizabeth Martino, but that is the info I was sent.
From Ronny Bodine:
John Bodine was born 3 March 1789 (according to the age on his gravestone, 32 years, 5 months, 9 days). He was buried in the Church of the Ascension Burying Ground, at West New Brighton, Richmond County. Married at the home of Benajah Martino (Moravian Church registers), Richmond County, to Elizabeth Martino, daughter of Benajah and Hannah (Decker) Martino. In the will of Benjamin Martino, of Castleton, dated 19 Oct 1814, he named his daughter Elizabeth and executors Hannah Martino, his wife, and "John Bodine, son of Vincent" (Richmond Co. Wills B: 576). Elizabeth was bapt. 27 Nov 1797 at the Moravian Church. On 22 Feb 1832, Gabriel Martino was appointed guardian of his nephew, Vincent Bodine (Richmond Co. Guardianships 1: 235).