What best describes the time period when the us had one political party?

There was never a year for one major party in the United States. Examples in 1787 there were the Federalist, later to become the Democrat's, and the Anti-Federalists, later to become the Republicans.

The Federalist's (now known as Democrats) believe in a strong 'central government', a government that holds the power and rights to give down to the people, as well as were for the 'central bank'.

The Anti-Federalist's (now known as Republicans) believe in a rights to the states, a government that the power comes from the people through the states to the federal government, and were against a 'central bank'.

There were many times that one party held both the legislative and executive branches most recently where the Obama Administration 2008-2010, Bush administration 2004-2006