Hugh Bay was born around 1836 in Ohio to Joseph and Sarah Bay. His father was a farmer who owned $2,000 of real estate by 1850. The family lived in Perry, Ohio, and he eventually moved to Indiana. He married Cordelia Ann Shell on August 28, 1856, and they had three children: Nancy, born on July 16, 1858; Sarah, born on July 18, 1860; and Mary, born on May 1, 1862. They lived in St. Marys, Indiana, and he worked as a farmer. By 1860, he owned $150 of personal property.
He enlisted in the Union army, and he mustered in as a private in Company K of the 89th Indiana Infantry on August 15, 1862. The regiment took part in the Red River campaign and the Battle of Nashville. He died in the latter battle on December 16, 1864.