I had earlier information saying he was born in 1789.
From Ronny Bodine:
From Marriage Records of Berkeley County, Virginia [now West Virginia]
Bond of 15 July 1811, no return, Abraham Burdine and Mrs. Polly Cross. Surety by Isaac Morlatt.
Abraham Bodine was named as the eldest child by his father in his 1825 pension declaration. Nothing is known of him prior to his marriage in 1811 to Mrs. Polly Cross. Berkeley County marriage records reflect the marriage of a Basil Cross to Mary Seaborn on 13 Feb 1800 and it appears this Basil was the son of an older Basil Cross (1750-1822) who died in Berkeley County and whose son must have died leaving his widow, Mrs. Polly Cross, to marry Abraham Bodine in 1811. It is not known if he accompanied his parents on their move to Warren County, Ohio in 1819 as further record of Abraham Bodine/Burdine or his wife has been found.