@TheCobbler,
During the reign of Elizabeth I Shakespeare’s company was called the Lord Chamberlain’s Men, this was because they were patronised by the Lord Chamberlain.
When Elizabeth died and James I became king they stopped being the Lord Chamberlain’s Men and instead became the King’s Men.
So Shakespeare was definitely in with James. Macbeth was written specifically for the King who had his own problems with witches and had even written a book on the subject. James was a direct descendent of Banquo, and in the play Macbeth asks the witches about his progeny as the witches had prophesied that Banquo would not become king but he would father kings.
When Macbeth asks the witches he is shown a long list of kings and some scholars believe a mirror would have been used to show James’ I reflection.
So yes, Shakespeare was on very good terms with James, and James commissioned that English translation of the Bible, so it is not at all inconceivable that Shakespeare had a hand in it.
However, nothing is proven either way.