I came across a couple of letters from John Bradshawe on the 'Net. They come from a site which claims to show the papers published by the Manx Society between 1860 and 1862.
The letters aren't very informative, but here are links in case they are useful for someone's research:
John Bradshawe to Colonel Duckenfield, 12 Dec 1651
John Bradshawe to Colonel Duckenfield, 23 Dec 1651
While on the subject of Bradshawe, readers with an interest in the trial of Charles I may be wish to know about The Tyrannicide Brief: The Story of the Man who Sent Charles I to the Scaffold (2005), by Geoffrey Robertson published by Chattos and Windus, pp448. This book is not about Bradshawe, but about the life of John Cooke, chief prosecutor of the king.
The first Bradshawe reference in this book is: "In 1646 Cooke teamed up with another obscure Puritan lawyer, John Bradshawe, to argue for the release from prison of the Leveller firebrand, John Lilburne. Robertson (p. 87) argues that this case established in English law the famed ‘right to silence’."