This quiet city of broad leafy boulevards is plastered with posters and slogans applauding Bulgarian-Soviet friendship, but it often seems that the best show in town is on the sidewalk outside the U.S. Embassy.

Much to the embarrassment of Bulgarian authorities, the sidewalk is always crowded with Bulgarians gazing at window displays in the U.S. Embassy Information Center. Every week a new photo exhibition covers nonpolitical subjects, from jazz to space technology. But what draws the biggest crowds is any insight into how ordinary Americans live.

Recently, for example, several hundred people gathered six deep outside the embassy trying to catch a glimpse of life in Granville, Ohio, despite the presence of a uniformed militiaman intent on moving them on. The exhibition explained the significance of such mysterious institutions as the Rexall drugstore, high school cheerleaders, and an automatic carwash.

It would be a mistake to conclude that Bulgaria is about to jettison its alliance with Moscow and embrace the Western way of life. But there are signs that after 35 years of copying the Soviet model, many Bulgarians are seeking to broaden their horizons.

The first impression that strikes the visitor to Bulgaria is that Soviet society is flourishing in the Balkans, scaled down certainly, but otherwise faithfully reproduced. The second impression is of a country whose exposed positions makes it at once more relaxed and open to outside influence that the Soviet Union, yet less adventurous than its unorthodox Communist neighbors, Yugoslavia and Romania.

On the surface, Bulgaria remains the very model of the Soviet Union's loyal younger brother, a favorite phrase of Bulgarian leaders. Bulgaria seems to have benefited politically and economically from its close ties with Russia, which go back to its liberation by czarist armies in 1878 following five centuries of Turkish rule.

Bulgarian leaders constantly inclulcate love for the Soviet Union among the country's 8.5 million residents. The annual May Day parade, for example is a replica of the Kremlin version - with the Bulgarian Politiburo gathered atop the mausoleum of longtime Bulgarian Communist leader Georgi Dimitrov, placards describing how workers have overfulfilled their plan by staggering percentages and a cacophony of stirring music.

Every portrait of the Bulgarian leader, Todor Zhivkov, whose 25 years in power make him the longest-living serving Soviet bloc leader, is flanked by an equally large portrait of Leonid Brezhnev. "From Centuries - For Centuries," proclaim the slogans. No one needs reminding that they refer to Bulgarian-Soviet friendship.

A sole reminder of Bulgaria's somewhat Ruritanian past is provided by the hussar-type uniforms on a goosestepping honor guard outside the masoleum. Said to have been designed by a former Bulgarian king, they resemble the ill-fated uniforms commissioned by Richard Nixon for the White House guard.

Looking at home in a sea of red banners is the Soviet ambassador, who occupies a post akin to what a Western colleague describes as "a viceroy to India." The former ambassador, Vladimir Bozovskii, has just returned to Moscow after a round of farewell parties attended by the entire Bulgarian Politburo. During his tour of duty, he frequently attended Politburo meetings and accompanied Zhivkov around the country.

Soviet economic assistance has furnished Bulgaria with more than 90 percent of its productive capacity in heavy industry and more than 40 percent overall. In 1977, 55 percent of Bulgaria's foreign trade was with the Soviet Union. The Kremlin supplies Bulgaria with more than 90 percent of its oil.

Bulgaria's economic system was integrated further with the Soviet Union's with the November opening of ferry service between the two countries. Operating across the Black Sea, the huge ferryboats - each has a capacity for 108 freight cars - eliminate long d lays for overload transport through Romania and could have strategic importance in the event of trouble elsewhere in the Balkans.

Combined with his long service, Zhivkov's unswerving loyalty has won him a special place in the Soviet bloc. He has been entrusted with several foreign policy missions on behalf of the Kremlin, and in the fall he will travel to Vietnam and Cambodia in a demonstration of the Kremlin's diplomatic support for the new rulers in Phnom Penh.

The ambivalence of ordinary Bulgarians toward official glorofication of the Soviet Union was expressed by a middle-class mother whose son returned from Sofia's elite Russian-language school boasting to his friends about the superiority of all things Russina. Proud that he was doing so well in class, she nevertheless took him to one side and rebuked him: "You are not a Russian, son. You are a Bulgarian - and don't you ever forget that."

Also irritating are governmental attempts to attribute all successes to the period of Communist rule since World War II but resurrecting the glories of the medieval Bulgarian state when convenient. A current joke runs: "Bulgaria has had 1,300 years of history - all in the last 35 years."

Zhivkov has stated flatly that Bulgaria has no dissidents. While there is no movement to match Charter 77 in Czechoslovakia or even the Helsinki monitoring groups in the Soviet Union, beneath the surface are undercurrents of discontent, indicated by the recent daubing of the slogan "35 years of slavery" on a building in downtown Sofia.

Of more immediate concern to Bulgarian authorities are mounting economic difficulties. Measured in terms of capacity to repay, Bulgaria's indebtedness to the West is greater than any other East European country. And despite the enthusiastic placards carried by workers on May Day, production has been running well below planned targets, particularly in heavy industry.

Even much-vaunted Soviet subsidies have a negative side. In the view of Western economists, they have distorted the overall development of Bulgaria's economy and left it ill-prepared to cope with sudden jolts such as the sharp increases in the price of Soviet oil that the Kremlin is imposing on its allies.

The economic problems are reflected in widespread shortages of many goods including basic foodstuffs such as meat, fruit, and vege tables. Although Bulgaria is an agricultural country with a food surplus, it sells much of its produce abroad to reduce the trade deficit.

Popular grumbling over meat shortages has become a sensitive issue for Bulgarian politicians, but they are at a loss to solve it. Looking on the bright side, a Western ambassador remarked recently at a diplomatic reception that eating less meat was good for the health. The remark was overheard by Zhivkov, who said, "If you can convince the Bulgarian people, we'll award you the order of Dimitrov."