George Bush is belatedly trying to make good on his 1988 campaign promise to be the "education president," and he's in a hurry to do it before the 1992 campaign.

His package of reforms relies heavily on the involvement of private businesses, and his new Secretary of Education Lamar Alexander is cozy in both worlds - public service and private moneymaking. If George Bush is the "education president," then Lamar Alexander is the "business secretary."His talent for moneymaking made some in the Senate nervous when they were called on to confirm Alexander's nomination. Privately, some Senate investigators complained that they didn't have enough time to analyze the implications of Alexander's business prowess. He made a long string of brilliant personal investments as governor of Tennessee and president of the University of Tennessee.

Some of those investments were analyzed superficially by the Senate, but the lawmakers wouldn't devote the resources to send investigators to Tennessee for a close look. Nor would the Republicans on the committee stand for a grilling of a candidate who was well-qualified in so many other ways. Alexander is a breath of fresh air in the office, but he is also a man who made millions of dollars on private investments while employed as a highly influential public servant. That is the side of the new education secretary that has to be watched, especially in light of Bush's plan to involve businesses more heavily in the school system.

Alexander says he makes a point of steering clear of conflicts of interest, but he may not steer clear enough.

On his first day as education secretary, he announced his vision of cooperation between schools and businesses, including the possibility that private corporations would run some public schools. And the two corporations that tripped so easily off his tongue were Burger King and Xerox.

Our associate Jim Lynch checked into Alexander's record with both companies. In 1988, Burger King gave Alexander its first national "Distinguished Service to Education" award with a $10,000 check. A spokeswoman for Alexander said he gave the check to educational causes and that the mention of Burger King as a possible school sponsor was "purely coincidental."

Burger King already runs alternative high schools in 10 cities and is shooting for a Burger King Academy in every community. Such an ambitious goal would not be possible without cooperation from the Education Department.

What about Xerox? One of Alexander's first hires was his top deputy, David Kearns, former chairman of the Xerox Corp. and a leading corporate advocate of education reform. A Xerox spokesman told us that the company has no immediate plans to get involved in the running of public schools.

Alexander's spokeswoman dismissed the notion that the proposed new role for businesses in public schools would raise conflicts of interest. But a Senate investigator told us that Alexander's plugging of Xerox and Burger King is a reflection of how cavalier he was about allegations of conflict of interest in his business dealings in Tennessee. "He has no sensitivity toward the appearance of conflict of interest," the investigator said.

Alexander calls himself a risk taker, but his investments have the look of a rainmaker. Perhaps Bush should have made him Treasury secretary where he could wipe out the national debt.