Sources & Information:

William BASSET (note spelling) -- " William Basset, of the Leiden Separatists, arrived in 1621 on the Fortune. In Leiden records, he is shown as a master mason, from Sandwich, Kent. He was a widower of Cicely Bassett, and he was betrothed in Leiden in 1611 to Mary Butler, with William Brewster, Roger Wilson, Anna Fuller, and Rose Lisle as witnesses, but Mary died before the marriage. he was betrothed on 29 July 1611 to Margaret Oldham, with Edward Southworth, Rober Wilson, Elizabeth Neal, and Wybra Pontus as witnesses, and they married 13 August 1611. He married in Leiden a third time to Elizabeth _________(Dexter, p. 165), and he brought her and their son William to Plymouth. Wife Elizabeth and children William and Elizabeth were in the 1627 division, but the wife died later. Basset married at Plymouth a fourth wife after 5 June 1651 Mary (Tilden) Lapham, for on that date Timothy Hatherly proved the will of Thomas Lapham, deceased. The widow Lapham, being weak, was not able to appear in court (PCR 2:169). Earlier, 22 June 1650, Mary Lapham, Widow of Thomas Lapham of Scituate, confirmed the sale of land in Tenterden, Kent, to Thomas Hiland (MD 10:199; PCR 12:194). The will of Timothy Hatherly dated 12 December 1664 (MD 16:158-59), left L5 to the wife of William Basset, "my wifes Daughter," and thus Mary would have been the daughter of Nathaniel Tilden of Scituate."
"On 8 November 1666 William Basset, who described himself as a blacksmith of Bridgewater, sold four lots to John Sprague of Duxbury, and Basset's wife Mary gave her consent, John Sprague being her husband's son-in-law (Ply. Colony LR 3:66). In his will, dated 3 April 1667, sworn 5 June 1667, William Basset mentioned his unnamed wife (Mary swore to his inventory), his son Joseph, and his son William's son William (MD 16:162; the inventory shows an interesting collection of books. On 2 June 1669 William Basset of Sandwich, oldest son of William Basset sometime of Bridgewater, deceased, confirmed land to his youngest brother, Joseph Basset of Bridgewater (Ply. Colony LR 3:140). William Basset, Sr. also had a daughter Sarah, who married Peregrine White, q.v.; a daughter Ruth, who married John, son of Francis Sprague, qv. (Tag 41:178); and a daughter Elizabeth, who married Thomas burgess in 1648 (PCR 8:6) and divorced him in 1661 after he was brought to court for an act of uncleanness with Lydia Gaunt (the first divorce in Plymouth Colony), and the Court allowed Elizabeth to keep small things "that are in William Basset's hands" (PCR 3:221). On 6 June 1683 Goodwife Sprague and her son John agreed about land which formerly belonged to John Sprague's grandfather Basset (PCR 6:109). Ruthe (Basset) Sprague married (2) a man whose surname was Thomas (TAG 41:179). William, Sr. also had a son Nathaniel 2 Basset. Robert Ray King, "The Family of Nathan Basset of Chatham," NEHGR 125:7, has to do with Nathan 3 Basset, the son of Nathaniel 2 Basset and his wife Dorcas Joyce, daughter of John. (Note: In correspondence, Robert S. Wakefield questions whether it was the same William Basset in all four marriages, and it is a surprisingly large number of Englishmen sharing a name with someone else that was resident in Leiden.)

Source: The book, Plymouth Colony, Its History & People 1620-1691, by Eugene Aubrey Stratton FASG, Former Historian General of the General Society of Mayflower Descendants. Ancestry Publishing, P.O. Box 476, Salt Lake City, UT 84110.

William Bassett is reported as a passenger on the Fortune, 1621.

William Bassett -- He was a gunsmith and worker in metals, and is probably the William, son of William Bassett of Bethnal Green, London, next Whitechapel, who was baptized at Stepney, 24 October, 1600. Extended investigation satisfactorily disposes of the inference that he was identical with a William Bassett of Leyden twice married before 1612 and said to be from Sandwich, Co. Kent. The church records of Sandwich, all parishes, do not confirm this supposition. The Emigrant's death in 1667 and the terms of his will indicate that he was not old enough to have been a widower in 1611, as was the Leyden William, who was a "hodman" (mason?). Bethnal Green was in the Pilgrim neighborhood whence came Hopkins, Warren and Snow. He was unmarried on arrival, but in the division of 1623 was allotted two acres showing that he had taken a wife before that date.

Page 106: WILLIAM BASSETT. The second share was surely for his wife Eliaabeth, and there is no reason to suppose that they were not married when they arrived. See article in The Mayflower Quarterly (May 1974), p. 56.

Source: The English Ancestry and Homes of the Pilgrim Fathers, by Charles Edward Banks, reprinted with addiitons and corrections, Genealogical Publishing Co., Inc., Baltimore 1984. Page 106.