The new factor in Washington's crippling teachers' strike is a tough-talking, hard-line union veteran named Robert P. (Bob) Bates, a crack negotiator and national trouble-shooter for the American Federation of Teachers.

Shortly after a 56-day teachers' strike ended earlier this month in St. Louis, Bates, who was accused by some critics of prolonging that strike, was given a new assignment, that of coming to Washington as a consultant to the striking Washington Teachers' Union and help move the on-again, off-again negotiations toward a settlement and away from what Bates' boss, AFT organizing director Chuck Richards, described as the "progressively worse" proposals being offered by school board negotiators.

Last Sunday, the union for the first time countered previous school board contract offerings with an unprecedented far-reaching proposal for expanded health and medical benefits and a 10 percent pay increase "If the board wanted to negotiate a contract instead of an end to the strike," one labor source said, explaining the proposal "then we'd negotiate a contract."

Two days later, when union leaders met with Mayor Marion Barry, it was Bates who did most of the speaking. At times, sources said, Bates even motioned with his arms for union president William Simons to stop talking. After the meeting, one aide to Barry said, there was some concern as to who was really running the strike - Simons or Bates.

School board negotiators, in a tactic that some veteran labor activists see as an attempt to discredit Simons, said Wednesday that they believe Bates is in charge, and that the once home-grown teacher dispute has been transformed into a cause celebre for national union organizers.

Bates, 43, described his role yesterday as one of bringing "imagination and resourcefulness" to a "polarized situation." Several local labor activits, saying that the school board's negotiators have been so confined by the stric orders from the school board that they cannot actively negotiate, believe the coming of Bates signals the coming of a quicker resolution to the strike.

"That fact that he is in town means that the seriousness of the thing has escalated," said Ray Edwards, an organizer for the rival National Education Association. "The signal to the employer is that you better get somebody at the table who's not fooling around."

But D.C. shool board members, school administrators, and even some members of the mayor's staff are concerned that Bates' active entry into this labor fray could mean for the District the same thing school officials in St. Louis said it meant for them.

"I honestly don't believe there was anybody here in town that was capable of doing the job he did," said Henry M. Grich Jr., vice president of the St. Louis school board. "He provided the backbone for the group to continue the strike. If it had been just our own people, it wouldn't have lasted as long."

"Did Grich say that?" Bates said yesterday, when asked for a response to his role in St. Louis. "Ask him two questions: When I came there did he have a settlement? When I left, did he have a settlement?"

Some school officials said yesterday that it appeared as if Bates and the AFT, which is headed by Albert Shanker had snatched control of the Washington strike from Simons.

A continually strong and hard-line AFT presence in Washington was necessary, those officials said privately, to maintain AFT's local dominance over its national rival, the NEA, in a city where the NEA actively lobbies as a national representative of the nation's teachers.

Simons has asserted that he alone is in control of the Washington strike, and Bates said yesterday that Simons, an AFT national vice president, had requested that he become a consultant to the local strikers.

Bates said the D.C. strike has national implications for the union because like many other strikes, it involves a struggle for control over educational policy. Bates said there was a "national conspiracy" to undermine union power, and in the District, he said, "I think School Superintendent*) Vincent Reed is the crux of the whole problem.

"It's Reed's attempt to urge the school board that he could run a miracle school system without the union," Bates said.

Some observers said yesterday that the participation of Bates in the bargaining could increase pressure on school board members to become involved in the negotiations themselves as Barry and the union have suggested.

Board members have said they are too divided and inexperienced to bargain successfully and have instead entrusted their negotiating to members of Reed's staff.

On Wednesday, Barry asked the city council to adopt a resolution urging the board to become actively involved in the talks and board members met that afternoon with members of council to discuss the possible legislation.

Yesterday, however, all 10 members of the board signed a letter to the council expressing the board's gratitude for the council's concern, but asserting that it is the board that has the authority to resolve the strike and that that could be done without council help.

The board has rejected the expanded proposal presented Sunday by the union. On Thursday night, the union rejected as "a demand that teachers surrender" a school board plan for an interim accord to end the strike.

Meanwhile, in yesterday's negotiations, the union offered its own plan for an interim agreement. The union had sharply rejected the school board's back-to-work proposal on Wednesday.

The new union plan goes back to the union's original demand - made when the strike began on March 6 - that its old contract with the board be continued, including the dues check-off, until a long-term agreement is reached.

In addition, Simons said the union wants a guarantee that no disciplinary action will be taken against striking teachers and that all those who lost pay because of the strike be allowed to make up the time by working additional days late this spring.

Simons read the proposal to board negotiators at about 1 p.m., and then read it to reporters at a news conference. Negotiations were scheduled to resume this morning.

Kenneth W. Nickoles, the board's chief negotiator, said no written copies of the union's new proposal were available before he also left for court at about 2 p.m.

Under the new union plan, a fivemember "blue ribbon" panel would also be created to make recommendations for reaching a long-term contract. Simons said the panel would include two representatives appointed by the board, two appointed by the union, and a neutral chairman agreed to by both sides or appointed by the Federal Mediation and Conciliation Service if they can't agree.

Simons said he had set aside temporarily the union's "escalated" demands, first made on Sunday, for a 10 percent wage increase and major improvements in fringe benefits, in an effort to get schools reopened quickly. But he said the union will press these demands before the proposed blue ribbon panel.

Yesterday D.C. Superior Court Judge Gladys Kessler told attorneys for the board and union that she would decide late Friday whether to impose a preliminary injunction against the striking union.