There is absolutely no connection as far as research can tell.Mary Bomar Younger died in 1818 in Halifax County, VA.Her family is pretty well documented in Halifax County and Essex County, VA from 1685-mid 1800's. She descended from Edward and Isabella Bomar of Essex. Her father was Bibby Bomar, son of John and Barbara Bush Bomar.Her husband, Williamson Younger, descended from William, Thomas and Alexander Younger.Alexander jumped ship in about 1675 and settled in Essex County, VA leaving a brother Andrew in Scotland.
The Younger brothers have a fairly well documented history in Maryland, Kentucky, and Missouri.Cole Younger was not born until Jan 15, 1834, and there are three generations of his ancestors documented before him that are not connected with Mary's family.
I hope I've answered your question, but if there's anything else I can help you with, please let me know.