William Bernard is the son of Francis Bernard, Esq.  born 1558, died 21 Nov 1630, his wife, Mary Woolhouse  daughter of Anthony Woolhouse. 
Col. William Bernard was born circa 1603 at Kingsthorpe, Northamptonshire, England.  He immigrated in the ship Furtherance to Virginia in 1622. 
He married Lucy Higginson, widow of [Major] Lewis Burwell and daughter of Capt. Robert Higginson and Joanne Tokesey, between 18 November 1652 and 1655.  They had one son, George, and two daughters: Lucy, (wife of Dr. Edmund Gwyn & of Edward Creffield); & Elizabeth, (wife of Thomas Todd). 
Col. William Bernard died on 31 March 1665 at of Nansemond, Virginia.  His widow Lucy married Philip Ludwell. 
William Bernard is double first cousin to Richard Bernard who immigrated from England to Virginia about 22 years after William. Being a double first cousin is the same genetically as being a sibling. William and Richard have the same grandparents - all four of them, because their fathers, Richard Bernard and Francis Bernard, who were brothers, married the Woolhouse sisters, Elizabeth and Mary.