James was Elizabeth's immediate successor and grew up speaking Elizabethan English.
His mother was Elizabeth's first cousin, Mary Queen of Scots, a Catholic. When Elizabeth had her beheaded, James was a child and Elizabeth took responsibility for his upbringing. He was, of course, raised and educated as a Protestant. On his mother's death, he became King James VI of Scotland and on Elizabeth's death he becamed King James I of England (which is why he is sometimes referred to as "King James I and VI"). Any bible written or translated into English in his lifetime would most assuredly use Elizabethan English.
But it was neither an accurate nor faithful translation, and several books were intentionally left out of the King's version (what the Catholics call "The Apocrypha").
If these guys actually knew the true history of the bible, they'd be mortified. It was put together by a Catholic pope, he picked the material that served his political purposes ignored the rest. It remained a CATHOLIC book until James, who intentionally removed certain books from the New Testament that did not suit him. Ironically, the largely homophobic religious right are passionately enamoured of a book commissioned by...and its development personally overseen by...a man who was known to take lovers of both genders.
Truth...she's a heartless bitch, eh?