BECAUSE OF growing taxpayer interest being directed toward the troubled finances of the District these days, some people may well ask just what the city's financial experts do all day. Good question. It happens that they spend alarming amounts of valuable time trekking to Capitol Hill to beg, borrow and grovel for permission to spend whatever money the city has raised on its own in the first place. It's an old tradition grown worse. The repeat performances of these fiscal exercises -- once for the House and again for the Senate -- have gradually become events of spring, summer, fall and winter.

We aren't even talking here of the congressional budget-cutters currently backing away at the annual federal payment to the city; that's yet another act. What really squanders time is the budget-hearing process. If the top ranks of city hall aren't up before the House appropriations subcommittee, they're over before the Senate counterparts. And if they aren't asking for a fiscal 1980 supplemental appropriation (translation: permission to spend a little more of what's around for the current year), they're either testifying on the fiscal 1981 budget request (which should relate to that supplemental request that hasn't been approved) or slapping together another request of some sort for the White House, which has to get a look before anything is sent to the Hill.

Once in a while, some member of Congress suggests the lack of any sense in this rigmarole. Two members of the House subcommittee, one the chairman and the other the ranking minority member, commendably did just that the other day. Rep. Julian Dixon (D-Calif.), who has recently inherited the chairmanship, says he doesn't think it's his job to dictate personal line-by-line budget orders to city officials. Rep. Carl D. Pursell (R-Mich.) says that "to sit here and look at line items on these detailed budgets is a waste of time."

Maybe these two men on the job haven't had a chance to get the hang of it. But then again, maybe there's some hope that this kind of congressional boredom -- which certainly helped to account for passage of the home rule charter, anyway -- will be infectious enough to produce an efficient procedure that respects the local authority this city's elected government should be exercising to manage its finances more effectively.