Metro's budget office had bad news yesterday for taxpayers in the the District and Alexandria: Shifting patterns of bus and rail ridership indicate that the D.C. share of the transit system's subsidy bills could go about $2.4 million higher, while Alexandria's may rise by more than $200,000.

But there was good news for the six other jurisdictions in the regional transit system. Their shares of Metro's total $177 million subsidy bills would hold about hold even or drop slightly.

The new figures, contained in a budget update report presented to a Metro board committee yesterday, were immediately challenged by officials in the District, which is already scheduled to pay $80 million in subsidies, and, like every other area jurisdiction, is battling to keep the lid on increases.

"We made a commitment" for about $80 million in this fiscal year's budget, said city transportation director Thomas Downs. "We didn't make a commitment for any more." Downs said Metro's calculations would be studied closely.

Alexandria's share of the subsidy bills would rise by $226,000 to about $8.6 million, according to Metro's calculations. An Alexandria official declined last night to comment on the estimate pending study of the figures.

Winners in the reshuffle would be Montgomery County, which would save $1.3 million, Prince George's County ($700,000), Arlington County ($435,000), Fairfax County ($81,000), and Fairfax City ($9,290). Falls Church's bills would remain almost steady, risng by about $650.

Metro is taking new stock of its financial state amid signs that revenues for its approved $339 million budget will be $11 million below target. The shortfall, officials believe, will be due to ridership that is running about 10 percent lower than expected, the deferral of a fare rise scheduled for January, and a poor showing in Metro's side business of running charter buses.

The report presented to the committee yesterday said that much of this shortfall could be offset by a partial hiring freeze and lower-than-expected expenses in such budget items as printing, production of tickets and transfers, and cost-of-living raises.

The remainder would be offset if pro-transit legislators on the Hill succeed in blocking the Reagan administration's plans to cut federal operating aid. In that case, federal operating aid would be about $5 million higher than expected. (Yesterday's budget report, in projecting subsidy savings and losses for the various jurisdictions, assumes that the extra federal money will be there.)

If all that came to pass, Metro's total subsidy requirements from local governments would hold roughly stable. However, changes in ridership would revise each jurisdiction's share.

In explaining the projected rise of the District's subsidy bills, Metro officials say the city appears to be caught in a long-recognized paradox in the subsidy formula under which a jurisdiction saves money if lots of its residents ride buses but loses money if lots of them ride Metrorail.

A Metrobus line generally operates with a particular jurisdiction agreeing to pick up whatever portion of the line's operating costs are not covered from fares. If ridership dwindles on a lines that D.C. is responsible for, fare revenue falls off and the subsidy the city must pay rises.

In the rail system, it works in reverse. The entire system's operating deficit is divided among the jurisdictions depending, to a large degree, on what portion of the riders resided in which jurisdiction. If the District's share of total rail ridership rises, so does its share of the subsidy.

Both forces have worked against D.C., Metro officials believe.

The city's bus ridership has fallen off, apparently because of its high rate of unemployment and the opening of the Red Line through to Van Ness. Additionally, D.C. residents form a larger proportion of the rail system's total patronage (up to 38 percent from an expected 35 percent), also apparently because of the line extension.

Metro officials are less sure about the reason for the rise in Alexandria's subsidy but believe it results from Metro's general ridership malaise.

In other action at Metro yesterday, the board approved a nonminority firm to run Metro's employe cafeteria, after lengthy discussion in which District board member Rev. Jerry Moore questioned staff members closely on notification and evaluation of minority firms.

Administration chief Carmen Turner said Metro drew on a constantly updated list of firms and that staff felt that the Boston-based Ogden Food Service Corp. would give the best service. The one minority bidder was qualified, she said, but was rated lower than Ogden.

Moore said that Metro procedures "tend to exclude a qualified minority" and that "it is with great reluctance that I am going to vote yes" for Ogden.