Vice President Bush continued his European campaign in behalf of the Reagan administration's "zero-zero" arms control proposal today, saying that it is the West that holds the high moral ground on this issue and challenging Moscow to come up with a better idea.

At a news conference in the Netherlands before flying here, Bush noted that "just yesterday" Soviet leader Yuri V. Andropov turned down a new offer by President Reagan to sign a zero-zero agreement, under which the Soviets would get rid of 600 medium-range missiles already based in Europe and the West would then forgo the scheduled deployment in Europe of 572 new American missiles.

"I think it's fair to ask," Bush said, "what's wrong with ridding the world of a new class of nuclear missiles?"

"If the Soviets have another plan that would seriously address this question, President Reagan has said we would give it serious consideration. But so far," Bush continued, "we have been offered a policy" by Moscow that allows only a Soviet monopoly on these weapons and no western counterforce.

The vice president appeared to be warming up to his role as the administration's public relations emissary to western Europe. He is consulting with allied leaders on the best way to reach arms agreement with Moscow and at the same time seeking to convince the European public that Reagan is sincere about arms control and counter efforts by Andropov to play on European fears and split the alliance.

"The only argument I've heard against the zero option," Bush told questioners, "is that the Soviet Union doesn't like it." That is not enough of a reason, he indicated, adding "We don't give up because Andropov says nyet."

To questions about whether sticking to Reagan's plan will ever lead to an agreement, Bush answered, "I say don't despair. Don't settle for the status quo. Let's be not only more idealistic but also more determined to reduce and eliminate this category of weapons. We have the strong moral position and people ought to be carrying signs" about that, he said in a reference to a few hundred demonstrators outside who were protesting the new American arms.

When asked how concerned he was about Andropov's "peace offensive," which seeks to make Moscow appear conciliatory, Bush said he "didn't mean to be cynical, but I'm thinking to myself of Afghanistan, of Poland, of human rights, of Jews persecuted. I'm thinking to myself, and this is a man of peace? But look, we are glad to hear it. I could say it's good they the Russians are talking about peace. But there are so many ways to prove it. So many ways to meet us even part of the way. But I have to confess I'm less than convinced."

Bush acknowledged that part of his mission was public relations. But he said he was proud of the zero-zero position and that this basic goal must not be allowed "to slip into the background."

He met privately in The Hague today for 90 minutes with Dutch Prime Minister Ruud Lubbers. In a separate news conference, Lubbers said his government supported the zero option but that this did not exclude preliminary agreements toward that goal.

The Dutch and Belgians are each supposed to receive 48 new U.S. cruise missiles. But there is strong opposition, especially in Holland.