Bulgarian Connection; The Time of the Assassins, by Claire Sterling. New York: Holt, Rinehart & Winston. 256 pp. $14.95. The Plot to Kill the Pope, by Paul Henze. New York: Charles Scribner's Sons. 224 pp. $14.95.

MORE than a year has passed since a possible ''Bulgarian connection'' to the 1981 assassination attempt against Pope John Paul II made front-page news, and the passage of time seems to have bolstered the view in the West that involvement of Bulgarian spies and possibly even the Soviet KGB was unlikely after all.

But now two new books supporting the theory of an East-bloc conspiracy have rekindled debate. ''The Time of the Assassins'' and ''The Plot to Kill the Pope'' are the result of painstaking research by experienced investigators. Claire Sterling is an American journalist living in Italy and an expert on terrorism. Paul Henze was a member of the National Security Council during the Carter administration and is now a consultant for the Rand Corporation in Washington. Both of their books provide convincing circumstantial evidence of the existence of such a conspiracy.

Each author began to probe the case shortly after the shooting in May 1981, and long before the convicted assailant, Mehmet Ali Agca, gave a delayed confession that put Italian investigators on the Bulgarian trail. It was not until Nov. 25, 1982, that Sergei Ivanov Antonov, the Rome station manager of Balkan Airlines, was arrested on charges of complicity with the would-be papal assassin. A few days later, the judge investigating the shooting issued arrest warrants on the same charges against two other Bulgarians, both diplomats at the Rome embassy, who had already returned home.

Both books contain detailed analysis of Agca's personality, his family, and his religious and political background. The first half of Sterling's book follows his trail from his home in Malatya, in eastern Turkey, to his student years at Istanbul University, his arrest for the murder of newspaper editor Abdi Ipekci, and Agca's spectacular escape from the maximum-security Kartal-Maltepe prison. Ms. Sterling also investigates Agca's year and a half of peripatetic travel through several European and Middle Eastern countries - where he always stayed in first-class hotels and never lacked funds. Then she examines his activities in the summer of 1980, a time when Agca had been in Bulgaria at the luxury Hotel Vitosha, reputed headquarters of members of the Turkish mafia.

The personality that emerges from Sterling's research (and from Henze's, as well) strongly conflicts with the theory that the man who shot the Pope was a solitary, religiously motivated lunatic. An excellent student, Agca paid little attention to his religious duties - rarely went to prayers at the mosque and even indulged in alcohol.

The two authors also pick apart what they say was a carefully orchestrated effort to build up Agca's credentials as a fascist. Although he was closely connected with the right-wing ''Gray Wolves'' movement (some of whose members have also been implicated in the attempt to kill the Pope), Sterling and Henze separately uncovered evidence of Agca's dealings with leftist extremists. Agca is revealed as a political neutral, the perfect type to enlist as a hired assassin.

The theory that the gunman was a lone, mad killer was discarded from the beginning by both the Vatican and the court that sentenced Agca to life in prison before the Bulgarian connection surfaced. More than a year after the shooting, Prime Minister Amintore Fanfani told Italy's Parliament that the Bulgarian connection ''was not a hypothesis but a fact.'' But the Italian government's belief in the conspiracy theory was not shared by other Western governments.

In the second half of her book Sterling deals at length with what she claims was an effort by Western intelligence agencies, especially the CIA, to play down talk of a Soviet-Bulgarian plot. She charges that the CIA waged a war of silence and indifference to ''manipulate public opinion'' and cast doubt on the validity of the leads followed by Italian investigators.

Sterling claims that, in the wake of former KGB chief Yuri Andropov's elevation to Soviet leader, Washington and other Western capitals feared that proof of such a conspiracy would upset the delicate East-West balance. This concern, she says, led to ''the triumph of bureaucracy over reason.'' She hints that she received veiled warnings from American officials in Rome not to push too far in her research.

As a result ''Italy was left alone,'' she writes, and ''spokesmen for the West were used to push a point of vital interest to the East, at the expense of a close Western partner and ally.''

In ''The Plot to Kill the Pope'' Henze brings a scholarly analysis to the historical and political background that could have led to the conspiracy. He describes at length the chaos into which rampant terrorism had plunged Turkey and, to a lesser degree, Italy during the 1970s, thus transforming the two countries into playgrounds for various secret services.

Henze also stresses the potential threat to the stability of the Soviet empire posed by a Polish-born Pope, especially with the emergence of the independent trade union Solidarity in Poland and with the Pope's declared desire to rally Roman Catholics throughout Eastern Europe, including the Soviet regions of the Ukraine, Lithuania, Latvia, and Byelorussia. According to Henze, the emphasis of the Roman Catholic Church on human rights could have proved ''attractive even to (Eastern Europeans) who (had) no interest in theology.''

At the end of their meticulous works, both authors conclude that perhaps the complexity of international relations will prevent the full truth from ever emerging.

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