A federal judge in Alexandria refused yesterday to block the Federal Aviation Administration and a Virginia bank from spending upwards of $2 million for the purchase of 12 to 15 buses to run between downtown Washington and Dulles International Airport.

District Judge Richard L. Williams denied a request for a temporary restraining order against the FAA and the bank, requested by Motor Coach Industries Inc. of Pembina, N.D., and set the bus manufacturer's lawsuit against both for trial Feb. 16. Lawyers for Motor Coach charged that funds for the purchase are in effect public monies and that government procurement procedures should be followed in the purchase.

But the FAA, which owns and operates Dulles, said the money is coming from about $3 million raised by the airlines during the last two years to improve transportation to and from the airport on the Fairfax-Loudoun county line. The contributions were made after the FAA announced in 1980 that it would waive about $10 million in airport landing fees to encourage greater use of Dulles.

First and Merchants National Bank of Richmond, which held the money for the FAA, independently selected another bus manufacturer, Eagle International Inc. of Brownsville, Tex., to supply the $160,000 buses, the FAA contended in court arguments. The new buses, which are supposed to be in service this summer, will replace a dozen aging buses now operated for the FAA by a private contractor.