The most authoritative biography of Queen Elizabeth is:

Queen Elizabeth The Queen Mother (1966) by Dorothy Laird

Other, more recent, books worth noting are:

The Country Life Book of Queen Elizabeth The Queen Mother (revised 1983) by Godfrey Talbot

The Queen Mother: A Biography (1981) by Elizabeth Longford

God Bless Her! (1987) by Robert Lacey

Queen Elizabeth The Queen Mother at Clarence House (1996) by John Cornforth