In honour of the French King that gave assistance during a war the county was named after his house, the "House of Bourbon".
Generally the backtracking stops there in the good old USA tradition of keeping it close to home.
Let's go that little step further down in time.
The Kings of France that had the tittle of "Lord of Bourbon" got that tittle thrue inheritance and marriages over many centuries.
A cute little village, Bourbon-l'Archambault, in France has a rather impressive castle where the Lords of Bourbon Ruled.
This was naturally not build overnight and therefore somebody must have payed for it.
The first Lord of Bourbon was born in 870 and was named Adhémar of Bourbon. He had kids, they had kids, married into houses and eventually ended up being Kings of France, Spain, parts of Italy and Holland, Luxembourg etc etc.
The origins of the Bourbon line was documented by Anthony Marinus Hendrik Johan Stokvis (1855 - 1924) in a work that can be found on this link: http://fmg.ac/resources/scanned-sources/file/101-s-0690-11
So that's as far as I have found it, but I'm sure many of you can dig further. The ancestors of Adémar were not called "bourbon" but have lineages with the Merovingians.