President Bush Opens Era of Public-Steward Politics. Shift from Reagan in style, tone, and substance grows more visible. POST-REAGAN WHITE HOUSE

BUOYANTLY, unselfconsciously, George Bush is ushering in the post-Reagan era with changes that appear to be evoking the approval of the American people. After the festivities and pageantry marking the presidential inaugural, political observers point to differences of style, tone, and substance that already are setting apart the Bush presidency:

A low-key inaugural address that lacked rhetorical flourish or drum rolls but conveyed a down-to-earth conviction and simplicity.

A White House graced by a silver-haired First Lady and swarming with children and grandchildren.

Frequent, easier meetings with the news media.

An emphasis on bipartisanship and a spirit of cooperation between the executive and legislative branches.

A shift of presidential focus to the country's humanitarian and social needs.

Even Democrats are impressed with the President's efforts to reach out across the political and social spectrum for an affirmation of national unity. It was not lost on them that on Inauguration Day a black Marine sang the National Anthem on the steps of the Capitol even as the city of Miami was reeling from riots, disturbances that spoke pointedly of the nation's racial ills.

``National-interest politics, public-stewardship politics - that's what this man is about,'' says Horace Busby, a Democratic consultant who was once a key aide to Lyndon Johnson. ``Bush was picking up on a broad and great theme of the middle and latter half of the 20th century - `unity, diversity, generosity.' Unity is the most important thing an American president has to be concerned about because the country has so many groupings, and you don't have a country worth having without unity. He must find ways to let diversity express itself - to be respectful and to be respected.''

Mr. Busby also notes that this was the first time an incoming President did not have to deal with war or cold war. There was no need for an evangelical revving up of Americans to prepare to fight an enemy or to build up the military. ``He did not define what it means to be free of war and the threat of war and how much that permits us to reorient our national energies,'' he says.

As Mr. Bush begins his first week in the Oval Office, he enjoys the public goodwill that accrues to any new president. Americans visiting Washington for the inaugural occasion were ebullient and warm in their praise of his modesty and friendliness, even while noting that there still are very few specifics on what the President intends to do.

``I question how many tangible issues he really identified,'' commented Charles Schaefer of Augusta, Ga., who voted for Bush. ``It was a good philosophical speech and set a mood. But what sort of agenda is he going to put forth?''

``He would be a good president for the education of children and the fact that we're raising tomorrow's leaders,'' chimed in his wife Nan. ``We're confident but waiting to see.''

Among Washingtonians, too, whose lives and careers tend to be centered on government, there is a kind of relief that the anti-establishment Reagan era is over and a more ``normal'' presidency is in the offing. Many Republicans share the mood.

``Bush's speech was splendid because it had a tone of civic responsibility and stewardship - things that have been overlooked in the recent era of rampant individualism,'' says former Secretary of Defense James Schlesinger. ``The public has grown indifferent to our public leaders, and he has reached out with a sense of community. This says that a community continues to need a government, and there's none of the bureaucracy-bashing you had before.''

In the midst of the inaugural uplift, Washington is also acutely aware of the deficit and other national problems that confront Bush - and the political battles that lie ahead, however genuine the talk from both ends of Pennsylvania Avenue about bipartisanship. Bush, for example, has conspicuously set a central presidential goal of fostering a ``kinder, gentler'' America. In doing so, he is seen to be moving in step with the public mood.

But, political analysts say, it is not clear how this will work for him politically, as it puts him on the same turf as the Democrats, who will have their own agenda for addressing the nation's social needs.

``Bush has shifted the battle onto the terrain dominated by the Democrats,'' says conservative political analyst Kevin Phillips. ``He is marching his troops into the field where they have the artillery and public support, and they will want to do more than the Republicans.''

Republicans, Mr. Phillips suggests, will be divided. Business groups, for example, will be unhappy about any proposals to make the private sector share the burden on such issues as day care and parental leave.

``He's obliged to govern in weakened political circumstances and where the basic ideological drift is moving toward the center,'' says Phillips, publisher of the American Political Report. ``It doesn't make it easy for a Republican president.... It will be a tough four years.''

However tough, lawmakers and administration officials voice hope for a new period of ``realism'' in the public dialogue about issues.

Budget-making is viewed as a particularly important area for honesty and candor.

``Bush has to show people that he will not play the Reagan game of fake budgets based on incorrect assumptions,'' says a senior administration official. ``He has to signal that his budget will be based on reasonably accurate economic projections.''