I thought I got the exact date from Family Search, but can't now find it.
This is from Geni:
Birthdate: between February 16, 1755 and February 15, 1756
Death: February 15, 1838 (82)
Great Crosthwaite, Cumbria, England (United Kingdom)
Place of Burial: Great Crosthwaite, Cumbria, England
Immediate Family:
Husband of Betty (Stockdale) Bowe and Jane (Dixon) Bowe
Father of John Bowe; Ann Bowe; Thomas Bowe; Sarah Bowe and John Bowe