Although the Reagan administration and Virginia politicians were quick to claim victory after Senate approval Friday of a bill transferring control of National and Dulles International airports to a regional commission, the price of its passage may turn out to be higher than expected.

In an effort to end nine days of debate on a bill that the administration expected to pass easily, Virginia's Republican senators were forced to accept an amendment granting airport employes the right to collective bargaining, a provision that guarantees them trouble at home. The measure now must go to the House of Representatives, where it faces stiff opposition.

The bill that emerged from the Senate differs in several ways from the original proposal by the Reagan administration. It provides for leasing the airports to a regional commission for 50 years rather than selling the properties. The measure also leaves open the possibility,that, at some date, the airports could be sold to the highest bidder.

But the collective bargaining provision, accepted without objection by Virginia Sens. Paul S. Trible Jr. and John W. Warner, is perhaps the most controversial.

"The words 'collective bargaining' don't make people in this state happy at all," said Virginia state Sen. Clive L. Duval (D-Fairfax), a key supporter of the airport transfer. "It is something that people are completely opposed to. I can only hope that people will weigh all the merits and realize how badly the authority is needed."

Virginia is a solid right-to-work state and prohibits collective bargaining among public employes. Dulles and National are owned by the federal government, and most of the 10,000 people who work at the airports are protected by unions. The amendment, as accepted by the Senate, would allow all current employes to retain those collective bargaining rights.

Under the results of a similar case, Virginia residents who work for the Metro transit system can be required to join unions despite the state's right-to-work law, a loophole that has irritated Virginia politicians.

Several other amendments designed to placate Senate opponents of the legislation also could hamper the bill's chances for passage in the House. Supporters of the bill have acknowleged that they will face a tougher fight in the House than in the Senate. Most observers say the measure has no better than a 50-50 chance of becoming law.

One controversial provision would extend the maximum radius for nonstop flights to and from National Airport from 1,000 to 1,250 miles.

The perimeter rule, as it is called, was first implemented in 1966 and was designed to protect Dulles from losing air traffic to National. Extending the limit would mean that travelers from Dallas and Houston could fly nonstop to National.

The extension is expected to spark a struggle between two powerful members of the House, Majority Leader James C. Wright (D-Tex.) and Rep. Gene Snyder (R-Ky.), the ranking minority member of the House Public Works and Transportation Committee.

Wright wants Texans to be able to travel to National without intermediate stops, and Snyder is afraid that the change would mean fewer stops -- and less business -- for the Louisville airport.

The amendment providing for the lease rather than the sale of the airports could make the measure more palatable in the House, even though it was considered a setback for the Reagan administration in the Senate. U.S. Transportation Secretary Elizabeth Hanford Dole had encouraged the outright sale of the two facilities for a total of $47 million.

That price tag came under heavy attack in the Senate. The House was expected to be just as reluctant to sell the airports, worth billions of dollars, for so little.

"I think the lease amendment will help us, and we were happy to accept it," said A. Linwood Holton Jr., the former Virginia governor who headed the commission that recommended the transfer. "It eliminates once and for all any allegation that this is a giveaway."