Between 16 July 1945 and 23 September 1992 the United States of America conducted (by official count) 1054 nuclear tests, and two nuclear attacks. The number of actual nuclear devices (aka "bombs") tested, and nuclear explosions is larger than this, but harder to establish precisely.
On October 2, 1992, the United States entered into another unilateral moratorium on nuclear weapons testing announced by President Bush. President Clinton extended this moratorium in July 1993, and again in March 1994 until September 1995. With the signing of the Comprehensive Test Ban Treaty in September 1996, the United States -- along with the other nuclear powers -- made a legal commitment never to test nuclear devices again, even though this treaty will likely never go into force due to the opposition of India.