Distilling was most likely brought to present-day Kentucky in the late 18th century by Scots, Scots-Irish, and other settlers (including English, Irish, Welsh, German, and French) who began to farm the area in earnest. The origin of bourbon as a distinct form of whiskey is not well documented and there are many conflicting legends and claims.
For example, the invention of bourbon is often attributed to Elijah Craig, a Baptist minister and distiller credited with many Kentucky firsts (e.g., fulling mill, paper mill, ropewalk) who is said to have been the first to age the product in charred oak casks, a process that gives bourbon its brownish color and distinctive taste. In Bourbon County, across the county line from Craig's distillery in what was then Fayette County, an early distiller named Jacob Spears has been named as the first to label his product as Bourbon whiskey. Although still popular and often repeated, the Craig legend is apocryphal. Similarly, the Spears story is a local favorite but is rarely repeated outside the county. There likely was no single "inventor" of bourbon, which developed into its present form in the late 19th century. Essentially, any type of grain can be used to make whiskey, and the practice of aging whiskey and charring the barrels for better flavor had been known in Europe for centuries. The late date of the Bourbon County etymology has led historian Michael Veach to dispute its authenticity. He proposes the whiskey was named after Bourbon Street in New Orleans, a major port where shipments of Kentucky whiskey sold well as a cheaper alternative to French cognac.
Another proposed origin of the name is the association with the geographic area known as Old Bourbon, consisting of the original Bourbon County in Virginia organized in 1785. This region included much of today's Eastern Kentucky, including 34 of the modern counties. It included the current Bourbon County in Kentucky, which became a county when Kentucky separated from Virginia as a new state in 1792. Numerous newspaper articles reference whiskey from Bourbon County, Kentucky dating as far back as 1824. According to the whiskey writer Charles K. Cowdery,
"When American pioneers pushed west of the Allegheny Mountains following the American Revolution, the first counties they founded covered vast regions. One of these original, huge counties was Bourbon, established in 1785 and named after the French royal family. While this vast county was being carved into many smaller ones, early in the 19th century, many people continued to call the region Old Bourbon. Located within Old Bourbon was the principal port on the Ohio River, Maysville, Kentucky, from which whiskey and other products were shipped. "Old Bourbon" was stencilled on the barrels to indicate their port of origin. Old Bourbon whiskey was different because it was the first corn whiskey most people had ever tasted. In time, bourbon became the name for any corn-based whiskey."
Read more at
https://en.wikipedia.org/wiki/Bourbon_whiskey.