The Fairfax County Board of Supervisors has agreed to study the value of starting a travel and tourist service for the rapidly growing county.

But Board Chairman John F. Herrity said he did not want county funds to pay for the bulk of operating a tourist bureau. "We have to move to work with the private sector and get them more involved financially," Herrity said in a telephone interview. "Part of the bill for promoting this has to be paid by [corporate and commercial businesses]."

Supervisor Joseph Alexander (D-Lee), who suggested a tourism study last June, said in an interview that the private sector was not "asking for a handout. We've been too busy promoting new industry. We're overlooking the goose that laid the golden egg."

Fairfax County is the only jurisdiction in the Washington area without an organized visitors service to actively promote its historical sites, parks, cultural activities, new hotels and restaurants. Until the late 1970s, county officials and business leaders said they were content with Fairfax County's image as a "bedroom community."

"There was a prevailing feeling in the county of no growth," said James Popino, president of the Fairfax County Chamber of Commerce. "Nobody was looking to promote Fairfax County in any way, shape or form. The attitude was 'bring up the drawbridge, I'm already here.' "

But in 1979, the potential for a bountiful tax base in commercial and industrial development was recognized and drastically reversed the "no growth" attitude.

According to the Visitor Services Study Committee's report, travelers in 1984 spent more than $240 million in Fairfax County, which totaled $3.4 million in tax revenues, without the help of a promotion bureau.

And in 1985, the report estimated that $285 million was spent by travelers in Fairfax County, or almost $4 million in tax revenues.

"We're now recognizing that a good return can be made to the county in the form of [millions of dollars a year] from [total] expenditures of about $200,000 a year," said John Lynch, chairman of the nine-member committee.

The Visitor Services Committee comprises county business leaders and citizens appointed by the board in June.

Lynch, who represented Fairfax County's Economic Development Authority on the panel, agreed that financial support of the proposed service should come from the private and public sectors.

Lynch said the county's Chamber of Commerce has already donated about $22,000 for brochures to highlight the county's historical and cultural attractions, hotels and restaurants, among others.

Lynch said if the county took the initiative in donating funds to the proposed tourism program he was certain more of the business community would do the same.

"The county's leadership is needed in starting the program. There will be private sector contributions, but the county's got to step out," Lynch said. "Obviously, the strong returns to the county are its own financial self-interest."

Besides expanding county tax revenues by millions of dollars, the committee's report suggested that a successful promotional service could ultimately result in thousands of new jobs in the hotel, retail and restaurant industries.

"Tourism includes shopping centers, restaurants and so on. There's one thing to bear in mind: We're already seeing $240 million a year [in travel expenditures] and that's without even trying," said Popino.

Currently, most visitors to the county are business travelers who stay near industrial or corporate centers for meetings or conventions. Lynch said the visitor service would try to attract more families and highlight Northern Virginia's less expensive hotel and motel room rates and its proximity to the District.

"The biggest weakness [in Fairfax County] is that a visitor to the metropolitan area doesn't recognize the county as a place to stay," Lynch said. "They go to Mount Vernon [George Washington's historic house in the southern part of the county] and return elsewhere for the night's lodging."