William Bundy was McGeorge's brother. He worked in the CIA until 1961, later with the Defense Department and, finally, as assistant Secretary of State for Far Eastern Affairs in the Johnson Administration.

Bundy recommended the bombing of North Vietnamese infrastructure and the blockade of Haiphong harbor as a means of deterring Hanoi's assistance to the NLF. Understanding that such action would require a formal declaration of war by Congress, Bundy's aides drafted a resolution in early 1964 granting the President virtual free rein in conducting the war. The resolution was passed by Congress later that year, spurred by the incident in the Gulf of Tonkin.

Biography of William Bundy (NY Times, May 29, 1964)
From Mark Bradley's Page at the University of Milwaukee
http://www.uwm.edu/~mbradley/wbundybio.html

Draft of the Gulf of Tonkin Resolution
From the Historian of the State Department
http://www.state.gov/www/about_state/history/vol_i/255_308.html (Scroll down to Doc. #278)

The National Security Council presented the President with a resolution, drafted by William Bundy's team, to be passed by Congress authorizing the President to "respond instantly with the use of appropriate force to repel any unprovoked attack against the armed forces of the United States and [...] to take [...] all measures including the use of armed force to assist that nation in the defense of its political independence and territorial integrity against aggression or subversion." Here is the final resolution as passed by Congress.

July 1, 1965 Memorandum from William Bundy to Johnson on future course of action
From Mark Bradley's Page at the University of Milwaukee
http://www.uwm.edu/~mbradley/wbundydoc1.html

Bundy recommends the "test" deployment of 85,000 troops in South Vietnam, and certain restraint in the bombing of North Vietnam, for diplomatic reasons. Bundy's was a "middle way" approach, a compromise between the hard-line position of McNamara and the more restrained way advocated by Ball.

July 10, 1965 Memorandum of Conversation, "Vietnam Panel"
From The National Security Archives at George Washington University
http://www.gwu.edu/~nsarchiv/coldwar/documents/episode-11/07-01.htm

Bundy organized a meeting of a group of consultants to discuss about future action in Vietnam. The experts concluded that South Vietnam was the first piece of the domino, and that keeping it from Communist control was essential for U.S. interests not only in Asia but also in Europe and globally.