Although the first Metro test train traveled all the way to National Airport station without problems yesterday, growing troubles back at the transit authority's headquarters raised doubts whether passengers will start riding the new route on schedule July 1.

Despite warnings yesterday that Metro's schedule department probably lacks time to prepare new timetables for connecting bus routes, the Metro board delayed action on a plan to reroute many bus lines to serve rail stations.

Moreover, the District government still has taken no ste psto provide about $10 million needed to subsidize the deficits of the rail operations after July 1, when the second 12-mile line to Virginia is added to the 5-mile route now operated in downtown Washington. Without a subsidy, Metro officials said the line cannot be run.

The lack of District funds has been known since last Sept. 16 when Mayor Walter E. Washington - a member of the Metro board - proposed a city budget for the next fiscal year that omits a subway subsidy, among other items.

The mayor said at that time that city taxation of suburban commuters or a regional tax would be nedeed to pay such costs. With no movement in either direction, D.C. budget director Comer S. Coppie said no action has been taken at city hall to fund rail service. The city budget must be approved by Congress, a time-consuming process.

At yesterday's board meeting, the Metro directors unanimously approved a $23.1 million regionwide subsidy for the subway as part of the transit system's construction and operating budgets for the fiscal year starting July 1.

No agreement has been reached on apportioning the $23.1 million among the regiin's local governments, but the city share probably will be about half the total.

The arrival of the first test train on the elevated tracks at National Airport, at an hour when the board was debating the bus-transfer plan, was a coincidence. Previous test trains had gone almost to the Pentagon.

Staff officials told the board that so much time has been consumed by the region's local governments in reviewing plans to divert bus routes to subway stations that Metro's 45-person scheduld department may not be able to prepare the necessary timetables.

William A. Boleyn, Metro comptroller, said the task is very complicated, since it includes the work assignments for all bus drivers, determining Metrobus payroll costs. He said the staff may find it hard to meet even an extended Aug. 1 deadline, a possibility that was discussed at yesterday's meeting.

"I do not accept what Mr. Boleyn just said," Joseph S. Wholey, Metro vice chairman from Arlington, replied, insisting upon meeting the July 1 schedule.

The bus-transfer plan, a modified version of proposals considered at public hearings last fall, would chiefly affect bus routes that would feed the National Airport, Pentagon and Rosslyn rail stations in Virginia and the Stadium-Armory, Potomac Avenue, Union Station and Rhode Island Avenue stations in the District.

Theodore C. Lutz, general manager, proposed that the changeover be stretched over several days instead of being put into effect immediately. Rather than approve the plan piecemeal, the board delayed action two weeks, putting a further squeeze on the schedule makers.