"BANKERS HAVE great leisure," Walter Bagehot wrote a century ago. "If they are busy something is wrong." There is currently a great deal of rushing around among the bankers, and, while quite a lot is wrong, in this case the busyness is a sign of hope. The Reagan administration is moving toward a much more active policy concerning the Latin countries' debts, and the commercial banks necessarily will have a crucial part to play in it.

A few influential bankers were invited to the Treasury last Tuesday evening for a chat with the secretary, James A. Baker. He wanted to talk to them before leaving for Seoul, where this week he is to lay out the new American proposal at the joint meetings of the World Bank and the International Monetary Fund.

The only way that the Latin American countries can carry their debts is through steady economic growth. With rising incomes they can make the payments on their loans, attracting further loans to be invested to produce still higher incomes and so on. That's the way the North American economies developed in the 19th century, and it is the way the Latin economies will develop in the late 20th century.

It's true that the banks lent too much in the years up to the crisis of 1982, and lent too much of it for unproductive purposes. That's why there was a crisis. The solution is not to cut off further credit; that threatens economic collapse in any modern economy. But something very much like that has happened. Net commercial lending to the largest Latin debtors was actually negative in the first quarter of this year, meaning that repayments to banks in North America, Europe and Japan were larger than the trickle of new loans from them. There has been only slight improvement since then. That's unhealthy for developing countries that need a reliable flow of new investment to keep production rising.

The new proposal Mr. Baker is taking to Seoul will apparently consist of a series of bargains. The Latin countries will be asked to undertake structural reforms to ensure that much more of any new credits goes into productivity, and much less into current consumption and political patronage. The rich countries led by the United States will support the World Bank in an increase of lending to support those reforms.

But there is not enough public money in the world to meet the credit requirements of economies as large and vigorous as Mexico's, Brazil's, Argentina's, and the rest. That will take private money, lent through the commercial banks. And that is why Mr. Baker wanted to talk to the bankers. There is a pretty good prospect that this series of bargains can be made to work but, as he knows, it can't be done by governments alone.