VICE PRESIDENT George Bush's trip through Europe this month to rally support for President Reagan's arms control proposals proved much about Bush, but not much about whether the world is heading for arms control or more arms race.

The trip demonstrated that the political skills that brought Bush from a political nowhere to the vice presidential nomination in 1980 are still sharp -- and can be used on a delicate diplomatic mission.

The vice president, who by choice dwells largely in the shadows of this administration, carried off a tricky assignment for the president at a particularly sensitive time in U.S.-European relations. Such a demonstration of his skills can only help Bush inside the administration, and could conceivably enhance his political future as well.

Reagan is known as "the great communicator," but his specialty is set-piece speeches. Bush, in a string of press conferences in seven European capitals, showed himself to be better than his boss at dealing with complicated and sensitive questions about atomic weapons -- the kinds of questions that have tripped up President Reagan in the past. The vice president was quick and articulate in handling or avoiding questions whose answers can cause bigger and more damaging headliness in a nuclear-sensitized European press than most Americans realize.

The skills Bush demonstrated are important in Europe. The often careless rhetoric about nuclear war and atomic weapons that came from the Reagan administration during its first year in office scared the populations in many allied countries and allowed an image of Reagan to develop as a trigger-happy cowboy. It is an image that the Soviets have sought to reinforce; Bush's mission to the allied capitals was meant in part to undo that portrait.

West Europeans are used to parliamentary systems where government leaders must be prepared to respond instantaneously to colleagues' questions without a prepared text in front of them.It is a system that, requires leaders to demonstrate a clear mastery of issues. By demonstrating a comparable talent in his public appearances in Europe, Bush no doubt reassured Europeans while enhancing the image of the administration.

"The flying ambassador," as Italy's influential, left-ofcenter newspaper La Repubblica put it, "is not obscured by the president's shadow."

In London's ancient Guild Hall, Bush drew applause from a large audience after he asked a challenger from England's leading disarmament organization: "Do you think we don't want peace? Do you think we care less than others about nuclear war?" It was a succinct way to put one side of the argument about the best way to avoid war. Bush's point was that military balance, even if it meant lots of weapons, was one way to keep the peace and that such a view did not mean that those who support it are any less concerned about nuclear war than those demonstrating against it.

Moments later a young man rose from the audience to ask about small battlefield atomic weapons, limited nuclear war in Europe and whether the dilemma for Europeans was to "surrender or sizzle."

Bush smiled and said "I'm not even going to repeat your question." It was answers to similar questions by Reagan, Defense Secretary Caspar W. Weinberger and former Secretary of State Alexander M. Haig early in 1981 -- all of which suggested that war could be limited to Europe -- that created the Reagan administration's image problem in Europe.

So in public, Bush played the role of an effective public relations man for the Reagan administration. In private, there is also reason to believe Bush handled himself well in his meetings with European leaders. His greatest accomplishment may well have been avoiding saying too much or asking too many questions.

Bush was sent to Europe by Reagan mostly to listen to what allied leaders had to say about the vexing and politically-explosive problem of trying to eliminate or limit the deployments of Soviet and American medium-range, nuclear-tipped ballistic missiles.

From what can be learned about these confidential talks, Bush did mostly listen, and the Europeans did not have too much specific to say. In effect, he didn't try to pry out of the Europeans the kind of message that might have put a lot of immediate pressure on Reagan to change his position in the deadlocked arms talks with the Soviets at Geneva.

That Reagan position is called the zero-zero plan. It calls for the Soviets to dismantle all 600 or so of their existing medium-range missiles in return for the United States foregoing the future deployment of 572 new missiles.

The Soviets have flatly rejected this solution and there seems no chance they will ever accept it. Everybody in Europe knows this, and knows that only a compromise agreement is feasible.

This fundamental fact of diplomatic life leads to be paradox of the Bush trip to Europe: Because it was successful as a public relations venture, it could wind up making an agreement with the Soviets even harder to achieve.

When Reagan first announced his zero-zero proposal in November, 1981, it was viewed in many western quarters as both clever and imaginative because it proposed elimination of an entire class of weapons on both sides. The large European anti-huclear movement was -- temporarily at least -- knocked off balance by Reagan's offer.But, as Bush acknowledged publicly, the West just let things slide afterward and left the propoganda field to the Soviets, who have done a very good job.

So it was part of Bush's assignment in Europe to refurbish the image of "morality and the basic soundness" of the zero-zero plan. By succeeding in doing just that, Bush probably postponed the moment when -- because of mounting political pressures in Western Europe and the United States -- Washington will feel compelled to move toward a genuine compromise.

Bush probably postponed that moment, but it remains in the offing. That is the Reagan administration's fundamental problem.

From Washington's point of view, Bush's short-term success was certainly welcome, not least because it might enhance the prospects of West Germany's ruling conservative coalition in the March 6 elections. The conservatives support the new U.S. missile deployment, so if they win on March 6, it is reasoned here, Moscow will realize it must negotiate more seriously to prevent or limit the new NATO deployment.

However, by longstanding NATO agreement, that deployment is supposed to commence at the end of this year. So buying extra time now only compresses further the period in which it would be possible to negotiate an agreement on one of the most complex arms control issues ever to confront negotiators. That period has now shrunk -- at best -- to the ten months from March 7 until Dec. 31. Since the beginning of SALT negotiations in 1969, no arms control agreement has been negotiated so rapidly.

Of course, negotiations could continue after deployment begins, but by then the situation will be even more complicated.