Prince William County, frustrated in its attempts to get more state money for its roads, will ask voters Tuesday to approve a $20 million bond referendum, the county's first for road improvements. Most county politicians say the referendum's chances for passage are uncertain.

Roads are considered the major problem in the fast-growing county, where commuters face daily traffic jams on state-maintained roads that are greatly in need of widening and repairs.

"The bond is designed to help us overcome some of the bottlenecks that are stifling our economic development," said Neabsco Supervisor John D. Jenkins. "Unless we have some more economic development in this county, our tax rate will never come down."

Fairfax County took the lead in 1981 in appealing to voters for permission to sell bonds to raise $30 million in extra road money. Fairfax voters approved that bond, as well as a $25 million bond issue for roads the following year.

Although road construction in most Virginia counties is the responsibility of the state Department of Highways and Transportation, the agency has said it does not have the money to keep pace with the needed road improvements in populous, fast-growing areas of Northern Virginia.

All seven Prince William supervisors are backing the bonds, which would fund nine projects throughout the county, ranging from engineering and design work to building a road where none currently exists.

Nonetheless, the referendum's chances of passage are uncertain in Prince William, where voters, wary of higher taxes, have rejected seven of nine bond issues since 1974.

Northern Virginia voters will decide a number of other bond questions Tuesday. In Fairfax, voters will decide on three separate bonds totaling $109.8 million, including $74.8 million for school construction and improvements -- the largest school bond ever to go on the county ballot. In Arlington, four proposed bonds totaling $30 million would help fund Metrorail's expansion, community improvements, parkland acquisition, and street and highway projects. Loudoun County voters will decide on two bond issues with a value of $13 million for construction and renovation of libraries and improvements to the county's solid waste landfill system.

The most significant of the nine road projects in the Prince William bond proposal are:

* Final engineering and construction plans for the Rte. 234 bypass, which would swing southwest of the city of Manassas, connecting Rte. 234 at Brentsville Road with Interstate 66.

* Widening Rte. 234 between I-95 and Montclair to a four-lane divided highway. It is currently a two-lane road.

* Traffic safety improvements to Rte. 234 between Manassas and I-66, including the connection of existing turning lanes to create a continuous, 1.7-mile third lane and extending left-turn lanes.

* Widening Davis Ford Road between Minnieville Road and Old Bridge Road to create a four-lane divided roadway. It is currently two lanes.

There are also projects to widen U.S. Rte. 1 near Occoquan, widen Smoketown Road near Davis-Ford Road, extend Liberia Avenue between Davis-Ford Road and Rte. 234, extend Hoadly Road near Dale Boulevard and prepare drawings to widen Minnieville Road.

The Prince William bond proposal has drawn vocal opposition from a loose-knit citizens group known as Taxpayers Against the Road Referendum, which charges that the county cannot afford to incur the debt for a series of projects that will not dramatically improve the county's transportation problems.

"We're not in the same financial posture as Fairfax County is," said Terry Emerson, a former county attorney and leader of the taxpayers group. "We can't afford it here."

According to county figures, the real estate tax rate could rise by 6 cents per $100 of assessed value in fiscal 1985 to finance the bond issue. That would mean an initial tax increase of $48 for a county resident with a home with an assessed value of $80,000, with rates declining after the first year. County officials say the actual increase would most likely be 2 or 3 cents, given other expected revenue sources.

County officials also estimate that the total cost to taxpayers over the 20-year life of the bond sale would be $41 million, assuming an interest rate of 10 percent. They acknowledge that the state highway department has estimated that solving all of Prince William's road problems would cost at least $300 million.

Each of the county's seven supervisors had about $2.8 million to target for road projects in their districts, leading to charges by the taxpayers group that the bond issue is a pork barrel. Opponents of the bond proposal contend that if the bond is passed, the state may not live up to its obligations to Prince William.

Kay Levine, an eastern Prince William activist who opposes the bond sale, said, "If we pass this road bond, the state is going to say: 'Well, Prince William can take care of themselves.' "

Supporters of the bond issue -- many of them in the eastern end of Prince William, where commuters are accustomed to clogged roads -- look to the referendum as a chance for rush-hour relief.

County elected officials generally rate the bond's chances for approval as questionable. Said Woodbridge Supervisor Donald E. Kidwell, a Republican: "It's got a better chance than Walter Mondale."