Washington — The so-called ''Bulgarian connection'' is getting a keen eye in Washington.
Officially, there is silence here about the mounting evidence of Bulgarian sponsorship of the May 1981 attempt on the life of Pope John Paul II.
But privately, more and more United States officials, analysts, and congressmen are inclined to endorse views expressed by Richard Pipes, retiring National Security Council Soviet specialist, that ''to me the evidence is very strong.'' In a cable TV interview last weekend, he added that he found it hard to see how a Bulgarian conspiracy could have been developed without KGB encouragement.
It is this potential KGB involvement - and the implications for Soviet leader Yuri Andropov, its former boss - that is attracting particular attention.
Italian Defense Minister Lelio Lagorio's comments this week were followed carefully. Mr. Lagorio minced no words. And those versed in intelligence matters put special weight on his revelation that the Italian security services noted a marked upsurge of Bulgarian coded communications at the time of the attack on the Pope.
A similar surge of Bulgarian communications took place during the kidnapping of US Gen. James L. Dozier last winter, Mr. Lagorio told the Italian Parliament Dec. 20. Professionals consider such intercept data, seldom revealed publicly, prime evidence of clandestine involvement.
But if the Bulgarians were involved can the Russians be far behind?
It would be hard to find a Soviet or East European specialist in Washington to argue that the Bulgarians could have been acting on their own. Bulgaria is the only East European country whose relations with the Russians have never been strained by popular revolt or by leaders wanting to go their own way. The KGB is known to have almost as much confidence in Bulgarian intelligence operatives as it has in its own men.
For the 15 years until the spring of 1981, the KGB was headed by the new Soviet leader, Yuri Andropov. The specter the London Economist raised in its issue of Dec. 11 - ''the ghost of reasoned suspicion'' that Andropov could have been the ultimate architect of the plot against the Pope - takes on a great deal more substance in light of the latest news from Rome.
''The Soviets already have their Vietnam,'' declares a former high US government official. ''Afghanistan is at least as intractable a problem for them as Vietnam was for us. Now it looks as if they have a Watergate on their hands too.''
The Watergate scandal of the early 1970s, which was entirely an internal US affair, pales beside a scheme to assassinate the world's most prestigious religious leader. How serious could the implications be for Mr. Andropov, newly risen to Brezhnev's mantle? That is a question Washington is only beginning to weigh.
When new information first began to flow from Rome, a few journalists speculated that anti-Andropov elements in Moscow might be feeding it in an effort to undermine him. This now seems unlikely.
Mehmet Ali Agca began opening up to Italian security interrogators nearly a year ago. This intelligent young Turk was apparently reluctant to say much very fast; he may still have been hoping to be rescued. But in September he identified his Bulgarian supporters from photographs Italian officials showed him.
Meanwhile, the Italians had been getting a rich harvest of information from Luigi Scricciolo, a union official arrested in February 1982 who confessed to having been a Bulgarian agent in contact with the Red Brigades. He also confirmed Bulgarian interest in the kidnapping of General Dozier. This kind of information built up over a year could hardly have been contrived by opponents of Andropov.
Like Richard Nixon in Watergate, Andropov may have no one to blame for his current predicament but himself. And he may be compounding it by his efforts to cloud the situaton. Under such circumstances, the appetites of potential rivals in the Kremlin could be whetted.
''That depends on how Western leaders react,'' says one Washington specialist. ''If they look the other way, ask no embarrassing questions, and display eagerness to get back to talking detente, Andropov will tough it out and nobody in Moscow will have the guts to challenge him. He could come out of this stronger than ever. ''
Will the excitement simply die down?
No one in Washington is sure. The Italians, who get high marks from security experts for their determined pursuit of this case, show no inclination to play down the implications of what they have learned or to drop the leads they have opened up. What has come out of Italy has already made clear the fact that the plot against the Pope was only the most dramatic facet of a web of conspiracy that included support of the Red Brigades and direct anti-American actions. Mr. Scricciolo has made clear that the aim was to destabilize Italy and render it useless to the Western alliance.
A small group of Turkey experts is also watching closely. The Bulgarian role in supporting terrorism and encouraging drug trafficking and arms smuggling in Turkey is well known. Mr. Agca, this group hopes, may also talk about his earlier activities in Turkey. Several men linked with him have recently been extradited to Turkey and Italy from Germany and Switzerland.
Analysts who follow Soviet propaganda are struck by indications of deep concern on the Soviet side. Over the past weekend the Soviet news agency Tass, in somewhat frantic fashion, repeated three times a statement dismissing implications of Soviet involvement in the plot aginst the Pope as ''a campaign totally steeped in lies.'' It claimed the US is trying to cover up its own support of violence at home and abroad.
This is not the first time such Soviet accusations have been made. While the Pope was recovering from Agca's bullets in June 1981, the Soviet-sponsored Italian language magazine Oggi printed a story implying that the US had tried to kill the Pope to punish him for failing to support US Middle East peace efforts. Every few weeks since, in obscure publications apparently ready to publish disinformation for a price, allegations of neo-Nazi or CIA connections (standard KGB fare) have appeared.