Vice President Bush today urged an exhaustive investigation to "get to the bottom" of the controversy over how material from President Carter's 1980 reelection campaign was obtained by the camp of his opponent, Ronald Reagan.

"I don't understand it," Bush said in an interview, "but my view is, clear it up, get to the bottom of it, clear the mess up and get it out. Everybody that's got his tail in the air and his nose on the ground sniffing it out, let them get satisfied . . . . Let the facts determine it, that should be the lesson from any experience in the past."

Bush's remarks clearly referred to cooperation with Justice Department and congressional investigations that are under way.

Bush has not figured in the controversy. He said today that he had been "out of it totally, thank heavens, literally not knowing about it . . . . "

Bush said that he was baffled at first by the furor, but that after the questioning at President Reagan's news conference last week he thought "maybe there's something to this. There's a lot of serious people asking questions and doing stuff . . . .

"The only answer," he said, is to have the matter investigated, "letting authorities look at it, cooperating fully . . . find out what happened--what's the charge and who is innocent and who is guilty--find it out."

Bush said his information on the matter is limited to news accounts of the unfolding dispute that have been appearing in the European press. He said he was questioned about the controversy once on his trip, by a Finnish journalist who compared the controversy to a local political scandal.

Although Bush professed no role in the matter, his political confidants in the White House are involved. One of them, chief of staff James A. Baker III, who led Bush's unsuccessful drive for the 1980 GOP presidential nomination, has acknowledged seeing some Carter material after joining the Reagan campaign. Baker said the material came to him from William J. Casey, then Reagan's campaign manager and now director of the CIA.

Casey has said that he never saw the disputed material, would have been suspicious of it if he had and would not have given it to Baker.

Resolving these contradictions must be part of any probe, Bush indicated. "Whoever's got any information, whoever's got any recollection, ought to give it to the proper authorities," he said. "That is the only way, whatever it proves to be, to get the matter properly resolved, open and out."