They were, after all, "sole mates" when they met last spring at the White House and Millie sat on Raisa Gorbachev's foot. Now, in further evidence of that "bonding," as Barbara Bush described the encounter, the First Pooch has sent the Soviet First Lady a copy of "Millie's Book, as Dictated to Barbara Bush."

Mrs. Bush carried a signed copy (presumably her signature, not Millie's) to Helsinki and gave it to Mrs. Gorbachev when they got together while their husbands conferred Sunday on the Persian Gulf crisis. At Helsinki University's library, when Mrs. Gorbachev saw an ancient map of Moscow, she pulled Mrs. Bush over to take a look.

"After all," she reminded the First Lady, "you're coming to Moscow, so you should see what it looks like."

The two may know something nobody else does. There's been speculation about such a trip but so far the White House hasn't announced one. Their paths crossed often enough on the campaign trail. Now, Barbara Bush and Kitty Dukakis once again are dogging each other's tracks onto the network morning shows, this time to plug their books not their husbands -- though viewers can expect some of that too.

Today, for instance, ABC's "Good Morning America" wrapped up the second installment of a two-part interview with Kitty Dukakis, who has written "Now You Know" (published by Simon and Schuster). The interview was taped by "GMA" last week before she and Massachusetts Gov. Michael Dukakis flew to Europe.

Tomorrow, "GMA" airs an interview with Barbara Bush on a variety of subjects, including "Millie's Book," the proceeds of which will go to the Barbara Bush Foundation for Family Literacy. That interview and another one tomorrow with "CBS This Morning" are scheduled for taping at the White House today. Kitty's turn with CBS comes next week.

Americans will be seeing and hearing a lot from both women over the next few days. Interestingly, publisher William Morrow and Co. is launching Barbara Bush's book in New York where media interest is expected to be more intense than in blase "hometown" Washington. The First Lady is flying up for the party but the "author" is not, which raises the question of whether Millie is being muzzled or is just bored with being a celebrity. Spokeswoman Anna Perez says it is neither. "Millie rarely travels with Barbara Bush on her business trips," Perez said yesterday.

Kitty Dukakis, on the other hand, will launch her book on Sept. 20 in Washington, not New York or hometown Boston, at a reception hosted by Robert A. Farmer, treasurer of the Democratic National Committee and former Dukakis campaign finance chairman. Now vice chairman of Cassidy & Associates, Farmer raised nearly $60 million for Dukakis in 1988, a record amount by a Democratic Party fund-raiser.

"Indeed," writes Kitty in her book, "he's the most successful fund-raiser in the United States, and, like all fund-raisers, has a bit of malarkey in him. Bob has got a big ego, which I love to tease him about, yet he's also one of the most giving human beings I've ever known."

The following day, on Sept. 21, Kitty will address a Woman's National Democratic Club luncheon.

Even Jimmy Carter, sitting at home in Plains, Ga., almost missed her, so brief was Rosalynn Carter's moment on camera at the Miss America Pageant in Atlantic City Saturday night. "I think it was a quirk of the camera," an embarrassed pageant spokeswoman said yesterday. "They tend not to dwell on anyone too long. It wasn't intentional."

The former First Lady was seated in the audience when she was introduced as recipient of the pageant's second annual $10,000 Women's Achievement Award for her work in mental health.

"It went so quickly," said the spokeswoman. "I wish they had concentrated more on her than on Bert Parks."

At a luncheon earlier, Mrs. Carter said the money will be matched by a group with which she is associated. She also said through her mental health program at the Carter Center she is working with television and motion picture writers to accurately portray those suffering from mental illness and the stigma surrounding it.

The first recipient of the award was another former First Lady, Betty Ford, who was cited for her work in substance abuse and breast cancer.

Raisa Gorbachev's other new best friend, former First Lady Nancy Reagan, will be dropping into Moscow with former president Ronald Reagan this weekend. President and Mrs. Gorbachev have invited the Reagans to dine with them, a Reagan spokesman said yesterday.

The Reagans flew to Berlin yesterday on a 10-day journey that will take them to Poland, East and West Germany and Italy. Among leaders the Reagans will call on are Polish Solidarity leader Lech Walesa and Pope John Paul II.

In Moscow, Reagan will address the Supreme Soviet and meet with students at Moscow State University. The Reagans and Gorbachevs last saw each other in San Francisco in June when the Soviet couple were on their way home from their visit with the Bushes in Washington. That time the Gorbachevs and Reagans had breakfast together.