He was born in Yorkshire, England and married the only daughter of Franklin in 1767, after immigrating to New York City in 1765. His wife, Sarah Franklin Bache (1743-1808), was widely known for patriotism and benevolent activities.
Their son, Richard Bache Jr., served in the Republic of Texas Navy and was elected as a Representative to the Second Texas Legislature in 1847. Another son was Benjamin Franklin Bache (1769-1798).