The following is all from footnotes on page 178:
'Four children were born prior to William's marriage to his second wife. The name of his first wife has not been found.'
This source points out that his second wife, Mary, was the widow of Francis Grissell of Charlestown (not Francis Griswold as in AEBK), and that the marriage entry published in the Vital Records of Cambridge, Massachusetts (1914-15) 'gives no date other than "16--" ' and cites AEBK for the date of 4 Jan 1653. Since 'Francis Grissell died in Charlestown on 2 Oct. 1652', and a deed dated 9 Nov. 1655 is the evidence for his widow having married William Bullard, 'the marriage of William Bullard and Mary Grissell occurred between 1652 and 1655 ...'
'Dean C. Smith in [AEBK] ... attributes to William Bullard a third marriage', which Stott and Hyde do not believe to be correct, as they indicate that second wife, Mary, widow of Francis Grissell, was alive in 1679 when William wrote his will.