The Ledyard Bill book does not have any info on the Bill/Bligh connection because it was written too early (1867).However, a later book on the Bill Family, written by Harry F. Bill in 1996, called "The Bills of Billtown" does contain a connection.
Caleb Rand Bill,(William Cogswell Bill, Caleb Rand Bill, Asahel Bill, Ebenezer Bill), born 31 July 1852, Billtown, Nova Scotia, died 21 August 1917 at Wolfville, Nova Scotia.He married Margaret Bligh, born 13 Feb 1852 and died 17 June 1938.
Their children were: 1.William Cogswell Bill, b. 18 Sept 1874, Billtown, NS, m.Ethel Mayhew, unk date, and d. 18 Apr 1937. 2.Margaret Augusta Bill, b. 18 Sept 1874, Billtown, NS. (Must be a twin?Or a typo?), m. Edward G. Shannon (Col.) 3.Jeremiah Emerson Bill, b. 30 Jan 1876, Billtown, NS 4.John Philip W. Bill, b. 1877 Billtown, NS, d. 1 May 1940. He m.(1) Josie Patterson, and (2)Inez Steele 5.Ethelinda Bill, born 1879.She married Frederick P. Bligh 6.Earl Gordon Bill, b. 23 Jun 1884, d. 18 Nov 1947, and m. Lucy Ethel Vanwart 7.Paul Bill, b. 1888, d.1927
That is all the information in this book.Have you seen the Bligh information given in Eaton's "History of King's County, Nova Scotia"?