I hope you have had several replies by now to your surname inquiry.
My comments are short. E-mail me if you need more info.
First e-mail Gayle Rose Mark at the "Bozarth Beacon", a family quarterly - Gayle is soooo informed, you can't go wrong by contacting her.Her e-mail is email@example.com
Second, just for fun, you will want to go to www.bozarth.org for some current family info.
Third, and more to your point.Not all, but most Bozarth's and Bozorth's in America have the same Alpha American - Lots of Bossard's, Bosworth's, Bozard's, Bozier's and other variants also have that same Alpha American.I am told, but I do not know for certain, that Jean Bossard in French is pronounced John Bozarth.If that is true it would explain a lot.
The known Alpha American ancestor is Simon Bozarth.It is thought, but not varified, that Simon is one of three children of Jean Bossard who were aboard the Peter and Anthony of London that landed in America in September 1700.
If Simon's father is Jean (and we are still looking for varification) the ship they were on was one of three ships carrying French Huguenot Refugees and landed in Virginia.
I suggest to you that if you do some research you will find that Simon is your ancestor.Simon, again, may be French - some of his descendants claim he was English on the basis that he lived most of his adult life and died in a small English settlement called Evesham, NJ and married a woman of English descent.He left a will that he signed naming all of his children and his wife (some say Mary was his second wife).Some say there are other children that he didn't name in his will.This seems very unlikely to me, but others disagree.I am unaware of any descendants of the others that may be Simon's children.
Simon didn't write his will, but he did sign it.He clearly could not write English and his signature on the will has possibly lead to some of the variants of his surname.
Some, if not all, of the descentants of his youngest son Andrew use the Surname Bosworth.
One of Simon's grandson's, Joseph Bozarth, Sr., served in the Revolutionary War using the surname Bosier.