In another forum, Harley Bissell wrote: "...the yiddish meaning of Bissell is "a little bit". The french meaning is "a greyish or graying brown haired man". The Huguenot Bissell is listed as Bysselle. I think it's mainly cause it's so darned hard to rhythm anything with Bissell. The poet only lived ten miles away and surely heard of Israel Bissell. While we're on name meanings here are some more. The Egyptians had people who led trained animals into battle. That word for that job title was Bissell (phonetically). A Jordanian man told me that my name means heroic in arabic (whatever flavor they use in Jordan). and finally a web search of the name Bissell reveals a Mina Bissell described as an Iranian. It don't get any curiouser than that folks."
That's as comprehensive a comment as I've ever seen on the origin and meaning of the name Bissell. Since we know that the English family (the grandfather of Captain John, plus 3 sons) came from Alsace-Lorraine (a region of France next to Switzerland) in the mid-1500s, the Bysselle spelling is quite likely to be the original. And I've seen its meaning given as "dark and tawny" or, as Harley wrote, "a greyish or greying brown haired man." All of the other stuff is ~highly~ speculative.
I do know that during the same period there was a completely different family or group of families in Germany going by the name Beissel or Beitzel, later Anglicizing the name to Bisel. These folks have tested out as a much different genetic group than the Captain John clan. Much different. There are also Buzzell, Bizzell, Bussell, etc., none of which are closely related genetically to Captain John et al either.
As for the Yiddish or Jewish connection, any given Bissell may well be Jewish or Yiddish, but during the colonial era, as others have pointed out, Biblical names were ~frequently~ used for children. Jeremiah, Jedediah, Isaiah, Joshua, Joseph, Benjamin, Daniel, etc., etc.--and the vast majority of these folks were good Protestants, whose parents reached into the Bible for inspiration in naming their children. I had a great-great-great-uncle uncle named Israel Inman, and his household was Methodist.
Roger Bissell, editor
Bissell Histories and Mysteries