If the General Services Administration hadn't run out of money, Vice President Bush said, it would have torn down the Old Post Office Building in the mid-1930s.

After years of trembling on its site, always in terror of the wrecker's ball, the Old Post Office Building was rededicated by Bush yesterday as part of The Nancy Hanks Center.

Said Bush, "Today marks perhaps the only time you will hear a member of this administration express happiness that the government went broke."

As a chorus to the speeches, the appealing Ditchley Bells rang at intervals. The culminating cacophony, 45 minutes of seldom heard bell changes, rang out to the more than 800 guests.

The ceremony marked three events.

* It was first public look at the interior of the remodeled great gray granite edifice and the first use of its magnificent auditorium since the bold remodeling design by Arthur Cotton Moore was accepted in 1977 under the direction of Jay Solomon, then-general services administrator.

* The Ditchley Bells, a 10-bell peal cast in 1976, were officially rung for the first time, pulled by the Washington Cathedral Ringing Society and the North American Guild of Change Ringers. Princess Alexandra, cousin to Queen Elizabeth II; Paul Channon, British arts minister; and Sir David Wills, Ditchley Foundation chairman, formally presented the bells to Congress, and the gift was accepted by House Speaker Thomas P. (Tip) O'Neill (D-Mass.), who was there, and Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), who was in Tennessee because of a relative's death.

* The dedication marked the 200th anniversary of George Washington's declaration of cessation of hostilities, ending the American Revolution. Yesterday, speakers talked of 200 years of American-British friendship, politely overlooking the War of 1812, when the British burned the White House and the Capitol.

In his dedication speech yesterday, Bush recalled the perpetual criticism the building survived. He said that The Old Post Office's "Richardson Romanesque" fanciful style, designed by Willoughby Edbrooke, was out of date before the building was finished, ended by the Columbian Exposition, which espoused neo-classical architecture.

And when the Federal Triangle was completed, the building, especially its tower, stood out like "a trumpet in a string quartet," Bush said. Shortly after the building opened in 1899, a prominent architect suggested dynamiting it.

Roger P. Craig, assistant postmaster general, yesterday said that at the building's 1899 dedication, the Washington postmaster, James P. Willett, fell to his death down the postmaster general's private elevator shaft.

Bush described the early days of the building, saying, "This vast space was used as a sorting floor. In the photographs men sit here in cane-backed chairs working through bundles of packages and letters. They wear black wool suits, wing-tipped collars and spats. Next to their desks hang their bowler hats. In one photograph the men looked damp. It was summer, and the huge ceiling fans were doing little but stir the heat."

But yesterday, red, white and blue bunting hid the unfinished construction in the great cortile, or atrium--the 99-foot-by-184-foot interior court, the most dramatic uninterrupted space in Washington.

An American flag hung down the great clock and bell tower. Guests, including Anglophiles, members of Congress and people from the arts and humanities, gathered behind the elaborate iron railings, and in the pit at the foot of the tower, down the steamboat-gothic stairs. On the arched balconies that surround the deep space, employes of the National Endowment for the Humanities, who have just moved into the building, left their offices to see the celebration. More than 196 feet above the ground, the glittering skylight reflected a changing canopy of clouds and sun.

Through the glass roof, visitors could see the mighty clock and bell tower, rising to 315 feet, higher than the Statue of Freedom on the Capitol dome, higher than any other structure in Washington, except for the sky-piercing Washington Monument.

Six years ago, the building's great skylight was tarred over, leaving a dark, cavernous pit below.. The tiles were cracked and the marble broken on the encircling floors. Debris from departing bureaucrats was strewn on the floors. A large photograph of J. Edgar Hoover peeled crazily off a wall. It was even speculated that the building had been last used by the FBI as a wire-tapping central.

In 1971, architect Moore suggested saving the building as a hotel. A preservation group called Don't Tear It Down rallied at the building in April of that year. In 1974, Bill Lacy, then head of the National Endowment for the Arts' architectural section, proposed to Nancy Hanks, then-Arts Endowment chairman, that the building be saved as a visual and performing arts center and used for endowment offices. In 1977, the GSA held an architectural competition and chose Moore for the remodeling.

This month, the Arts and Humanities endowments, the Institute of Museum Services and the Advisory Commission on Historic Preservation are moving into offices on floors two through nine. The Pavilion of shops and restaurants on the lower floors, designed by Benjamin Thompson, is expected to open in September.

The presentation of the bells, based on the 1596 Westminister Abbey bells that cheered Britain during World War II, was the culmination of two days of ceremonies by the Ditchley Foundation.

Monday night, former British prime minister Alec Douglas-Home said, in the annual Ditchley Lecture, "I do not believe there will be a war, provided America and Britain and our allies keep our nerve and poise."

At a black-tie dinner afterward in the State Department's Diplomatic Reception Rooms, Secretary of Defense Caspar W. Weinberger said that if the two countries fulfilled "our responsibilities, the bells will always stand guard and witness to the rights of the individual."

Earlier Monday, Princess Alexandra climbed the Old Post Office tower to see the bells, accompanied by William Theobald, who engineered and installed them. At dinner Monday, wearing an amazing emerald festooning a pearl choker, she toasted the president of the United States after the Americans led a toast to the queen. Last night, the princess and her husband, Angus Ogilvy, dined with the Reagans and 22 others at the White House.

This fall, the building, its plaza and its performing arts stage at the base of the clock tower will be dedicated to Nancy Hanks. A bill passed in Congress in February, a month after Hanks' death, named the Old Post Office Building, its plaza, grounds, commercial and performing areas and the clock observation tower The Nancy Hanks Center.

A glass elevator is expected to be installed next year to carry visitors to the observation tower.