The earliest attempt to provide some biographical information about the King James translators was undertaken about 1650. I have a copy of the five-page manuscript, and talk about it during my King James Bible Conference presentations. Many of the older large histories of the English Bible give some information about the translators. The oldest book on the King James Bible that gives information about the translators is Vindication of Our Authorized Translation and Translators of the Bible; and of Preceding English Versions Authoritatively Commended to the Notice of Those Translators (F. C. & J. Rivington, 1819), by Henry John Todd. Chapter 7 is about the King James translators. The book is mainly a defense of the King James Bible “occasioned by certain objections made by Mr. John Bellany in his late translation of the book of Genesis, and by Sir James Bland Burges, in his reasons in favour of a new translation of the Holy Scriptures.” Todd supplemented this work with An Authentic Account of Our Authorized Translation of the Holy Bible, and of the Translators: with Testimonies to the Excellence of the Translation (J. G. and F. Rivington, 1834). It is termed on the title page the second edition. Todd says in his preface that it has been fifteen years since he wrote his first work, and that he has “now also made some additions to that account of the present translation.” The book is really an entirely new work. Chapter 2 is about the King James translators. I have reprinted both of Todd’s books in my Classic Reprints series. A third edition of the latter was issued in 1838. Although the book has been re-typeset, and contains two additional pages (70 verses 68), there is no difference between the second and third editions. I have seen another re-typeset but identical edition of 64 pages published in 1842 by the Society for Promoting Christian Knowledge with no edition number. This leads me to believe that there have perhaps been other editions issued by other publishers over the years.
Next there is The Translators Revived; A Biographical Memoir of the Authors of the Holy Bible (Charles Scribner, 1853), by Alexander W. McClure. Although the bulk of this book is about the King James translators, there is also information about the translators of the earlier English Bibles. I have an undated exact reprint by Maranatha Publications (Penn.) with a one-page foreword, but have seen the original. I also have an undated exact reprint by Maranatha Bible Society (Mich.) with a foreword and a brief history of our English Bible by R. E. Rhoades, and the addition of a bibliography. It claims to be taken from the 1858 edition, but this is probably a mistake, since I know of no other edition but the first of 1853.
The best book on the King James translators—and one that is only about the translators—is The King James Bible Translators (McFarland & Company, Inc., Publishers, 1982), by Olga S. Opfell. I own a signed copy of the undated paperback edition that was issued sometime after the year 2000 (the image on the cover has a copyright of 2001). Although she died in 2008, I did not know about her death until I received a letter from her husband in 2013. McFarland still sells two of her other books that it published (Queens, Empresses, Grand Duchesses and Regents, 1989; Royalty Who Wait, 2001), but The King James Bible Translators is out of print. I should note here that McFarland is the publisher of English Language Bible Translators (2003), by 
someone I know from the International Society of Bible Collectors named William E. Paul. Here is the publisher’s description: “It provides information about the men and women who produced English language translations. Arranged alphabetically by surname, each of the 346 entries includes biographical and vocational information; notes on the various editions produced; samples of their translation; and other pertinent facts. In cases where translations were done by committee, the chairpersons and project initiators are covered. Important anonymous translations are also included.”
The most recent book about the King James Translators, but not exclusively, is God’s Secretaries: The Making of the King James Bible (HarperCollins, 2003), by Adam Nicolson. This book was first published by HarperCollins in Great Britain the same year with a different cover design under the title of Power and Glory: Jacobean England and the Making of the King James Bible. A paperback edition of the latter was issued in 2004, and of the former in 2005, but with yet another cover design. The book was reissued in paperback for the quatercentenary of the King James Bible in 2011 under the title of When God Spoke English: The Making of the King James Bible (HarperPress, 2011). God’s Secretaries is readily available and highly recommended.
Another place to find out biographical information about the King James translators is the old Oxford Dictionary of National Biography. It is online for free here. The new edition cannot be accessed for free.