Benjamin Franklin Bosworth was born in 1801 to Olive and Alfred Bosworth in Saratoga Springs, NY. He was a student at Lenox Academy, a college preparatory school, from 1818 to 1821. Although he attended Union College in Schenectady, New York, it is neither known when he graduated nor where he attended medical school. He became a doctor and settled in Boston, New York. In 1832, Benjamin's son, Franklin S. Bosworth, was born in Boston, New York. Two years later, Benjamin's wife, whose name is unknown, died of consumption, and Benjamin left his child with his grandparents in Saratoga Springs, New York.

In 1836, Benjamin and his brother, Increase Child Bosworth, moved to Chicago. Three years later, in 1839, their parents and Franklin S. joined them, settling in Dundee, Illinois. Around the same time, Benjamin married again, giving up medicine for business pursuits, and became a merchant in McHenry, Illinois. The name of his second wife is also unknown. He had two daughters in this marriage. In 1843, Benjamin Franklin Bosworth died in McHenry, Illinois.

Benjamin Franklin Bosworth's daughters died shortly after their father's death. Franklin S. Bosworth was raised by his grandparents in Dundee, Illinois. Increase Bosworth, Benjamin's brother, was a merchant in Dundee and took care of his brother's estate. Franklin S. Bosworth was the father of Edward Increase Bosworth (A.B. (Yale) 1883, B.D. (Oberlin) 1886, A.M. 1893, D.D. 1901; d. 1927), former faculty member and Dean of the Oberlin Theological Seminary, 1883-1927, and great-grandfather of Edward Franklin Bosworth (A.B. 1916, B.D. 1923; d. 1957), former Dean of College Men at Oberlin College, 1927-1946, and Dean of Men, 1946-1956.