In my opinion you don't really need to read anything else on the Bodyline series itself if you read Frith's book but "The Larwood Story" and Jack Fingleton's "Cricket Crisis" take the story a little further.
There is, however a book being published very soon called "Bodyline Hypocrisy" which claims
"Through conversations with Harold Larwood, the main proponent of leg theory bowling on that tour, and by examining closely the private letters, thoughts and statements of many of the main protagonists of this infamous series, Arnold re-examines widely held beliefs and shatters many preconceptions as to the truth behind that incredible series which almost led to Australia leaving the Commonwealth. In this controversial book Arnold will scotch the belief that fast, leg-pitched bowling was what won the series for England, and puts forward a new and astonishing proposal - that the Aussies bottled it, disguising their failures under the welter of abuse hurled at England captain Jardine"
It is written by Michael Arnold of whom Amazon says "Michael Arnold is a well-known (not sure about that one tbh) English cricket writer, who now lives in Australia. Uniquely (sounds a rash statement) qualified to see the Bodyline series in its historical context, he also writes for Australian newspapers and broadcasts on radio."
Later on this year a full biography of Larwood is due from Duncan Hamilton who recently wrote an acclaimed biography of that favourite adopted son of Nottingham, Brian Clough. I am looking forward to getting both although I have rather higher hopes of Hamilton than Arnold - but you never know - there may be some revelation there - can't see it myself though