Jefferson County, New York is adjacent to Lake Ontario in upstate New York. Watertown is the county seat.
You can manipulate the 1860 census in many ways. What I did was to enter all letters in the surname beginning with the letters BO in Jefferson County, New York. However sometimes the O gets confused with the A as an example.
I found nothing even close to BB. Again in my opinion nothing in the 1860 census to establish his whereabouts. It is true that he could have living in an adjacent county to Jefferson County, New York.