Corrected to Tyrell County NC because of time of birth. I have review the Washington Co, NC 1778 Tax Records and there are none named Bowen on those records. See https://wctnarchives.org/1778-tax-list-captain-ganns-company/
"The county was formed in 1729 as Tyrrell Precinct of Albemarle County, from parts of Bertie Precinct, Chowan Precinct, Currituck Precinct, and Pasquotank Precinct. It was named for Sir John Tyrrell, one of the Lords Proprietors of Carolina.
With the abolition of Albemarle County in 1739, all of its constituent precincts became counties. In 1774 the western part of Tyrrell County was combined with part of Halifax County to form Martin County. In 1799 the western third of what was left of Tyrrell County became Washington County. In 1870 the half of Tyrrell County east of the Alligator River was combined with parts of Currituck County and Hyde County to form Dare County."
from source of https://en.wikipedia.org/wiki/Tyrrell_County,_North_Carolina
I will trust you are right. I get confused with all the county changes. I just know he was born in long acre township, Washington, Beaufort County NC. 1790 Beaufort NC census record shows 2 John Bowens at that time. 1st John Bowen has 1 male 16 and up, 1 male 16 and under and 2 females (this is not the father of Elisha John Bowen). 2nd John Bowen has 4 males under the age of 16, I male over the age of 16, 3 females and 1 slave. This John Bowen and the ages and gender of children match the father of Elisha John Bowen.