Michael Dukakis, back in Boston for the first time since winning the Democratic nomination, was greeted wuth cheers today when he walked into his Statehouse office. Republican George Bush, meanwhile, was getting mixed reviews as he sought to shore up support among women.

About 20 workers in the executive chamber cheered and applauded as Dukakis arrived at work at 8:50 a.m. today. He grinned and bowed and then spoke briefly to them before heading into his office.The Massachusetts governor, returning Sunday night from a three-day campaign trip, was greeted warmly by about 150 people in soggy weather at Boston's Logan International Airport.

Dukakis and his running mate, Lloyd Bentsen, traveled to five states, including the key fall battlegrounds of California and Texas. They set off on their inaugural campaign trip last week, just after accepting their respective nominations at the Democratic National Convention in Atlanta.

The Republicans, meanwhile, were looking ahead to their own convention, which opens three weeks from Monday in New Orleans.

Bush, the certain GOP nominee, was back in Washington after spending five days on the road. His campaigning between now and the opening of the GOP gathering will be curtailed because he has spent nearly the legal limit for pre-convention campaigning.

But White House spokesman Marlin Fitzwater said Sunday that President Reagan probably will campaign in the Midwest on Bush's behalf between now and the convention.

That word came as Reagan was flying back from California on Air Force One. Also aboard was Treasury Secretary James A. Baker III, who had been in California for a weekend fund-raiser, and his presence fueled new speculation about an imminent departure from the administration to run Bush's campaign.

Fitzwater said Baker had "a very brief chat" with Reagan and added: "He's still treasury secretary, put it that way."

When reporters sent Baker a note asking him to come back and talk to them about the matter, he sent back a dollar bill and suggested that reporters take a close look at the banknote bearing his signature.

Later, asked by reporters to "share the news," he responded: "There's no news to share."

Baker's status isn't the only source of speculation surrounding the Bush campaign. The vice president traveled to Albuquerque, N.M., on Sunday with former Transportation Secretary Elizabeth Hanford Dole, who has been mentioned as a potential running mate.

But campaign manager Lee Atwater said Bush won't reveal his choice of a running mate until next month in New Orleans.

"He's going to keep his own counsel on it, and he's going to let us all know at the convention," Atwater said Sunday in an interview on the CBS-TV program, "Face the Nation." He added that he thought an announcement then would be "very exciting and very dramatic."

Bush, in Albuquerque to speak to an organization of professional and business women, unveiled an ambitious $2.2 billion child-care plan that would be phased in over four years. The group's president, Beth Wray, welcomed the plan but tempered her praise by calling it "one of his first concrete gestures" toward women.

When Bush finished speaking, many in the audience broke into chants of "E-R-A" - a reference to the Equal Rights Amendment, which the vice president opposes. He also was presented with a red purse, which organization members said signified the gap between the earnings of women and men.

Dukakis, for his part, encountered anti-abortion protesters at a stop in St. Louis on Sunday, as he had a day earlier in Modesto, Calif. The governor supports a woman's right to an abortion.

"It's a difficult, very serious, very important ethical and moral judgment," Dukakis said at a news conference inside the church building. "But in my judgment it is a woman, in the exercise of her conscience and religious beliefs, that has to make that judgment."

In St. Louis, Dukakis and Bentsen were introduced by Rep. Richard Gephardt of Missouri, a onetime rival for the Democratic nomination. Gephardt accompanied them to the church he had attended since childhood.

"The most important thing in my life is family," Dukakis told the congregation. "They are our anchors. They are the place in which we get our strength. It was our parents that gave us our sense of values, sense of ethics, our sense of morality," he said.

Later, Bentsen and Dukakis stopped in Erie, Pa., where Dukakis continued to stress the theme of economic opportunity and commitment to the family. The governor called on the crowd of nearly 10,000 to help build "the strongest, the finest grass-roots organization that has ever been put together in a presidential campaign."

Dukakis seemed sure the time was right for his populist message - equal opportunity, family, good jobs, housing and education - to play well nationwide.

"I think what you see is not a request that government do everything but that government be a part. That's the kind of partnership we hope we can build beginning in January 1989," Dukakis said.

After the Pennsylvania stop, Bentsen returned to Washington. He was expected to campaign on his own later this week.