THANKS TO THE perseverance of an able mediator and the ultimate good sense of warring members of the YMCA family, a bitter local conflict over the Y's responsibility to the Shaw neighborhood appears resolved: there will be a new facility built adjacent to the now-vacant Anthony Bowen Y. It is up to the people and businesses of this city to chip in and make things happen as swiftly as they can.

On Thursday, the board of directors of the Metropolitan Washington YMCA--the group that originally voted to close the Bowen Y--took the crucial step, agreeing to start planning a new $1 million facility next to the old building. This was in the package that mediator Sterling Tucker had proposed. As outlined, tentative plans include a basketball court, day-care and classroom space and other facilities for the young people the Y serves.

Whether $1 million will be enough at today's prices is a question. So is the public's commitment now that matters are on a constructive track. In suggesting that the mayor step in and resolve this crisis, we recognized that private contributions would have to be forthcoming. And as part of the plan proposed by Mr. Tucker, the mayor's representative, there is to be a fund-raising campaign, which the mayor and other city officials will help to lead.

The rest of Mr. Tucker's plan is important, too: it calls for the city to give land to the YMCA for a full- service facility--possibly the Emery playground at Georgia and Missouri avenues NW, a site the Y has long sought. The city would take title to the old Bowen building and preserve it as a historical landmark.

So if all goes well, if all parties uphold their ends of the bargain, there can be dramatic, lasting improvements in the Y's record of constructive service to this city's youth. What better way to do it than with facilities and programs that the young can see, use and appreciate in the neighborhoods where it counts most.