Reconstruction of the pothole-pocked Woodrow Wilson Bridge is moving close to reality. The House of Representatives approved a bill yesterday granting $60 million for the job. The Senate is expected to concur promptly, today, sending the measure to the president.

His signing of the measure would open the way for an early start of the 2 1/2-year reconstruction project. An aide to Rep. Marjorie S. Holt (R-Md.), who played a leading role in the authorization, said all the work would be done at night to avoid rush-hour problems.

The span, which crosses the Potomac River at Alexandria, is part of Interstate Rte. 95, the major north-south highway on the Atlantic seaboard and a vital commuter artery. It carries about 89,000 automobiles and 19,000 trucks on an average weekday.

The legislation authorizes spending from the national Highway Trust Fund without need for a separate appropriation bill. The Wilson Bridge provision is included in a nationwide highway authorization bill.

When the bill originated in the House last year, extending the highway program for one year, it lacked the Wilson Bridge provision despite efforts by Holt to include it. The Senate rewrote the bill to authorize a multiyear extension, and at the joint urging of Sens. Charles McC. Mathias (R-Md.), Paul S. Sarbanes (D-Md.) and John W. Warner (R-Va.), added the Wilson Bridge authorization. The House chopped the measure back to one year but kept the bridge item, thus requiring Senate concurrence.

The Wilson Bridge is the only span on the interstate system owned by the federal government rather than by a state. Normal maintenance and operation is provided by Maryland, Virginia and the District of Columbia, since the bridge passes through all three jurisdictions.