Eula Bingham had just finished a speech to a group of farm broadcasters when a man popped up from the audience and offered his version of high tribute.

"I can tell," he exclaimed enthusiastically, "you're not the kind of person who's going to put out pamphlets on the dangers of slippery cow manure."

Bingham had received more tasteful bouquets since she took over the Occupational Safety and Health Administration, an energy with a portfolio of bureacuratic horror stories ranging from 35 pages of rules on the design of "exit" signs to bulletins telling farmers what they already knew about barnyard hazards.

But she laughingly accepted the tribute to the unstaffy, unbureaucratis "common sense" approach she is trying to instill in OSHA - an endeavor that has thus far won her endangered agency a new lease on life.

It has also turned a spotlight on one of Washington's more unorthodox new power-weilders: a onetime Kentucky farm girl who went on to become a nationally recongnized expert on industrial health problems but who still wears crazy-shirts to professional meetings, most recently one emblazoned with "OSHA Needs You! Enlist Today" at an American industrial flygienists Association meeting in New Orleans.

She lugs groceries back on the plane fron Cincinnati after weekends at home with her daughters and brings lunch to work in a sack. She pops in on aides, chase personal mail that's gotten lost in bureaucratic channels and laughs a lot, often at herself.

Told that she was one of only two assistant secretaries to be interviewed personally by President Carter before being appointed, she said her first reaction was "What other agency could possible be in that much trouble."

Bingham who did her won share of criticizing OSHA from her academic perch at the University of Cincinnati's medical school before coming to Washington last March has already disarmed many of OSHA's severess critics.

Many are skeptical that the changes will be more than cosmetic but appear willing to give her time to prove them wrong.

"When people ask what's good about OSHA, I say Eula Bingham," said James D. Mckevitt. Washington counsel for the National Federation of Independent Business, Inc., whose more than 500,000 small-business members have been in the forefront of OSHA critics since the agency was created in 1970.

"She's done her homework and she's got common sense," McKevitt said. "She's opened-minded and she listens . . . We've still got our fingers crossed, though . She seems too good to be true."

Bingham's main problem may be to live up to her initial rave notices - to follow through on the expections that she and Labor Secretary Ray Marshall, backed up by Carter, have raised for the agency in vowing to make it work as Congress intended.

With considerable fanfare, she aaanounced that OSHA will concentrate on serious health hazzards in high risk industries such as manufacturing and petrochemicals and downplay the "nitpicking" safety rules that made the agency so easy to laugh at.

She promised to quicken OSHA's snail's pace in issusing standards foe worker exposure to carcinogens and other dangerous substances, kicking off the effort with a quick move against contact with benzene.

She ordered a simplifying of paper work chores for employers, virtually eliminating them for small business operators. She plans by September to issue a lengthy list of minor regulations - "the so-called Mickey House rules that burden employers without protecting workers" - that will no longer be enforced.

She is prodding the agency to put more emphasis on education, voluntary compliance, consultation, coordination and expertise on the part of inspectors - all of which has been promised before but never delivered, causing the skeptics to reserve judgement.

An example is OSHA's own effort to train up to 200 industrial hygienists a year, through a comnination of graduate studies and on-the-job experience, to meet an acute shortage of such trained personnel - a shortage that was caused in part by the creation on the agency itself. The training program was begun last year by Bingham's predecessor, Morton Corn, but may not bear fruit in time to cope with Bingham's immediate goal of shifting from minor safety problems to sophiscated health hazards. OSHA has 150 or more vacancies for inspectors to fill this year.

There is also the basic issue of ferderal intervention, which some employers and conservative groups may continue to oppose, no matter how smoothly OSHA runs. A suit is now pending before the Supreme Court challenging the agency's authority to make unannounced inspections. OSHA says that authority is crucial to getting voluntary complaince.

Another question is intentions vs. results. "The question is not what she says in Washington, but what they dotics - whether she masters the buin Kansas City," said one of the skepreaucracy or it master her."

In the first round, it was Bingham 1, Bureaucracy 0, after a tough fight.

When she came to work at the Labor Department, someone routinely channeled all her personnal mail for someone else to answer. This went on until a message from a friend trickled through.

"It said something to the effect that, if you'd call off your minions we'd like to have you address our group, signed, Love . . .," she recalled recently. She called staff meetings, three of four of them. "They'd say, 'Look, this is no way we do the mail here,' and I'd say, 'No, this is not the way you do may mail here.'" Now she gets her mail, although she still has to track down an errant letter now and then.

Born in 1929 and raised on a farm after her father lost his railroad job during the Depression, Bingham led and early life that was remote from her future career in industrial health

She winces now at reminders of her 4-H project: growing tobacco. But her background was one of fatherly encouragement to set high goals and to pursue them."He never assumed I couldn't do something just because I was a female," say Bingham, who was a late but enthusiatic recruit to the cause of women's rights.

She helped put herself through college with part-time jobs that steered her into toxicology research, leading to a full professorchip at the University of Cincinnati and consulting work in environmental health, including an appointment to OSHA's advisory committee on cock-oven emissions.

Although she never worked for labor organis zations, she became an ally of industrial unions in promoting aggressive efforts to eliminate serious on-the-job health hazards. She was recommended by unions for the OSHA job but was not the first choice of most of them.

She speaks of ehr work with almost missionary zeal:

"I feel, I feel very strongly," she said the other day, "that people in this country should expect, as a matter of right, a safe and healthy work-place . . . When I hear these stories about human rights, I think, my God, workers have a right to expect they won't be killed on their jobs. If that means I should have to pay 50 cents - or $2 - more for my refrigerator, then I wouldn't want to hide it."

Thus far Bingham appears to be Carter favorite, Labor Secretary Marshall quotes the President as having said recently that "few things the government had been doing domestically have gotten as favorable a public response as Eula Bingham's efforts to transform OSHA."

But Anthony Mazzocchi, legislative director for the Oil Chemical and Atomic Workers Union and a colleague of Bingham from her pre-government days, views the acclaim wryly. "It's sad commentary on our society," he said, "when a person acts like the law intended and, my God she becomes a celebrity."