The public offering of one million shares of Columbia Air, a new airline based at Baltimore/Washington International Airport, has been abandoned.

Columbia officials said they will seek private financing for their initial operations, still scheduled for early 1982.

In making the announcement, Dan A. Colussy, chairman of the new airline, said he had been advised by E.F. Hutton & Co., the chief underwriters for the initial public stock offering, that it couldn't be completed at this time.

But Colussy expressed confidence that he would get the money he needs to start service. "I have been encouraged by the strong support we have received for the Columbia concept from both the public and institutional investors," he said, adding that Alex. Brown & Sons, Baltimore-based investment bankers, has been engaged to arrange private financing for the airline.

"Columbia Air will continue its plans for a start-up in early 1982," he said.

The offering was scheduled for earlier this month but was postponed following the filing of an amended prospectus. It contained new information that Air Florida had taken 9.9 percent equity in the new airline and that a major international airline--Scandinavia Airlines System -- intended to purchase 14.3 percent of the proposed offering.

Columbia had plans to begin service in January from BWI to New York, Boston and Pittsburgh with fares between 35 percent and 45 percent below existing coach fares. Columbia, many of whose officials came from Pan American World Airways with former Pan Am president Colussy, has the authority to operate to 31 cities from BWI.

A New York investment banker, who declined to be named, suggested that the public offering may have failed at this time because of the market's distrust of the Columbia concept at a time when the understaffed air traffic control system has limited significantly commercial airline access to 22 major airports.

In another BWI development, Texas International Airlines said last week that it will begin the only nonstop service between BWI and Kansas City on Dec. 1 with a $129 "Peanuts fare." The airline also is instituting the only one-stop service from BWI to Mexico City on that date.