The correct answer to your question is false. Here's what really happened. In 1964, the first year of the Lyndon Johnson administration, the destroyer USS Maddox (DD-731) engaged three North Vietnamese P-4 torpedo boats, resulting in damage to the three boats. This incident is significant because it lead Congress to pass the Gulf of Tonkin resolution which granted Johnson the authority to assist and Southeast Asian country who he considered jeopardized by "communist aggression". This meant that U.S. forces could be used without a declaration of war. The resolution was used by Johnson as his legal justification for escalating and continuing the war in Vietnam.
In 1964, American ships were attacked in the Gulf of Tonkin, but it was President Johnson that responded by sending bombers to North Vietnam.
President Kennedy was not alive in 1964. And we never sent bomers into North Viet-Nam at that time. The American ships were attacked and took action.