The tree from the unifier of Wales -  (FULL listing)

 Two princes carried Wales through these difficult years, Owain Gwynedd in the north and Rhys ap Gruffydd in south Wales. Both were aware of the complex problems to be faced: to deal with rival Welsh dynasties, to deal with marcher lords, and to live in the shadow of a rich and powerful neighbor. Owain gauged the political realities of the day quickly and, however often he had to yield, he did not lose the initiative.

Probably, John Wynne built Bodwrdda in the late 1500's (blue line below), and, in the mid-1600's, Hugh Bodwrda (red line below) adopted the manor name as a surname, replacing Gwyn.  At the time, a Sir John Wynne was laying claim to the North Wales-Gwynedd-Gwydir, legacy, back to Llelenyn and David ap Gruffyd, the last two true Princes of Wales.  These Gwyn/Wyn seem to have been based nearer Conwy, while the Bodwrdda clan was further west. 

The red line notes Bodwrdda Manor (red line) near Aberdaron on the Lleyn Peninsula of Northern Wales.

The obvious conjecture is that Reice Bodurtha was the son of  one of Hugh Bodurda's younger brothers.

Agawam, Massachusetss
Reice Bodurtha and Blanche Lewis were married -- 1645.  
Their children were A. Sonne, b. 3, 14, 1646 -- Buryed, 1. John, b. 3, 13, 1647. d. 3, 30; 1648, 2. Joseph, b. 1, 15, 1649; 3. Samuel, b. 10, 1, 1651; 4. John, b. 4, 12 1654. -- Drowned March 18, 1683.

The first mention of Reice Bodurtha, the ancester of all in this country bearing the name of Bodurtha or Bedortha, is found in the early records of Springfield, Mass., in the year 1641.  From what port he sailed, and where he landed on these Western shores is unknown.  The name indicates a Welsh origin, and the traditions held by several distinct branches of the family corroborate this view.

Much discussion has prevailed over the correct spelling of the name, but the earliest signatures yet found give the name unequivocally Bodurtha. In the town records it is spelled Bedorden, Bedorda, Bedortha, Bodurtha, Bodortha and Bedurtha, according to the fancy of the recorder seemingly. Those who bear the name will testify to the difficulty which all strangers meet in its pronunciation, and to the variations which are often heard.

Taking into account the fact that, in the early days of our country, the art of writing was by no means universal, and that the ear was depended upon alone, for the transmission of names, it will not seem so strange that these changes should occur. In the early days of the Springfield Colony, or Plantation of Agawam, as it was then called, when no stranger was allowed to remain more than ten days without vouchers, Reice Bodurtha must have satisfied the jealous guardians of the public peace of his honesty and good intentions, for he was granted a lease of land in 1644, and in the year following, 1645, he was granted a house lot by the Plantation. This house lot lying on West side of Main Street, Springfield, extended from "Ye streete fence to Ye great river," Lombard street marking its south boundary (according to Henry M. Burt).

The year 1683 was a fateful one in the family, for in March, Reice, a son, and the wife of another son, were drowned in crossing the Connecticut.  The story of this tragic event as preserved by the family, is that the three were returning from public worship on the Sabbath, when their canoe was upset, and they found a watery grave. It is said that the same day "public prayers had be n put up" for the safe passage of Reice Bodurtha to England, whither he intended to sail for the purpose of receiving a legacy lately left him. The preparations for this long voyage even to the Suwarrow boots made for this great occasion are narrated.

The Bodurtha Legacy was believed in by several successive generations and served as a foundation for many a castle in the air.

Note that Reice did not die in Suwarrow boots.  General Suwarroff had not been born in 1683.

The Book of the Feet - A History of Boots and Shoes