Jeffery Bell is an earnest young conservative egghead who aspires to be a legisator. But every time he runs, he runs into a legend.

He runs in New Jersey, where the mine-run politicians are legendary only for their larceny. But when he first tried for the U.S. Senate in 1978, Bell bumped up against the legendary "Dollar Bill" Bradley, Princeton Rhodes scholar, basketball all-star and fan favorite with the New York Knicks.

This year, he is trying again, and he finds himself the underdog in Tuesday's Republican senatorial primary to the legendary Millicent Fenwick, a/k/a the real-life Lacey Davenport of "Doonesbury" comic strip fame. Fenwick was plucked from the obscurity of the House of Representatives by "60 Minutes," People magazine and a hundred newspaper feature writers and transformed into a creature of popular legend: the plucky, pipe-smoking, pacemaker wearing, 72-year-old grandmother who stands up to anybody in Congress in her unrelenting war against secrecy and special privilege.

How do you fight that?

If you are Jeff Bell, you fight it by attempting a high-low mugging of the deceptively frail-looking dowager and you learn, to your chagrin, that the sweet little old lady knows a few jiu jitsu holds of her own.

Bell, 38, who worked for President Reagan from 1974 to 1976 and drafted the 1976 version of Reagan's federalism initiative, shares his old boss's belief that ideas can win elections. This year, Bell's idea is that the Federal Reserve Board must be induced to lower its discount rate and cease its open-market operations if interest rates are to be cut and Reagonomics given a chance to succeed.

Lacking Reagan's gift for anedotal persuasion, Bell substitutes a dogged professorial style that leaves some members of his audiences like the two dozen GOP leaders of rural Warren County, who heard his spiel in Hackettstown the other night plainly puzzled.

Fenwick and her pollsters find no signs that the idea is taking hold. In her last debate with Bell, in Glassboro, she dismissed the whole issue by saying, "I don't care about these theories. We've got to get people back to work."

Bell encountered similar skepticism when he used the then-obscure issue of a three-year, across-the-board tax cut as his main weapon in upsetting veteran Sen. Clifford P. Case in the 1973 GOP primary. Encouraged by seeing Reagan embrace the policy in 1980 and Congress pass it in 1981, he told an interviewer, "Maybe you run the risk of being a one-issue candidate, but that is one more than most candidates ever establish."

Even though he was beaten in the general election by Bradley, Bell did well enough that he was an early-book favorite for the 1982 nomination for the seat vacated by the Abscam conviction and resignation of Harrison A. (Pete) Williams Jr. (D).

But polling for the 1981 gubernatorial election showed Fenwick had attained a degree of fame and favorable reputation throughout the state that was extraordinary for a four-term House member. A woman of wealth and elegance, with a cultivated Tallulah Bankhead voice and seemingly unquenchable enthusiasm, she became a standout--even in the 1974 class of House mavericks--for her independent, outspoken disdain for politics-as-usual.

She fought leaders of both parties on their fondness for congressional perquisites, and won a reputation as a quick-witted defender of the taxpayer's dollar even while piling up a record unusually liberal for a House Republican.

Told by her doctor last fall that she was fit as a fiddle, Fenwick plunged into the Senate race and quickly soared into a 30-point lead over Bell in Bell's own polls.

Knowing, as he said, that "I can't possibly win a personality contest against Millicent," Bell has tried to make their race a test of Republican orthodoxy.

Not all of it is as elevated as his seminars on Federal Reserve policy. For the past three weeks, his campaign saturated the air waves with $600,000 worth of ads claiming that Fenwick "voted for Jimmy Carter's policies more often than most Democrats in Congress" and had the highest rating from Americans for Democratic Action of any Republican in the House. They whacked at her opposition to the death penalty, school prayer and many major weapons systems.

This week, voters got a picture of Bell with Ronald and Nancy Reagan and an updated quote from Reagan saying Bell's "work, dedication and ability are greatly needed in the United States Senate."

Earlier, the Bell campaign mailed out postcard-sized pictures of Fenwick with ex-Rep. Bella Abzug (D-N.Y.) and a text reading: "When radical leftist Bella Abzug left Congress, Millicent Fenwick said, 'I feel like I've lost a strong right arm.'"

Last week, the diocesan newspaper here carried a large ad criticizing Fenwick's positions on abortion, tuition tax credits and school prayer. The headline: "If She Wins, Catholics Lose."

Bell disavowed that ad, placed by an independent-expenditure group called "New Jersey Pro-Life PAC," and said in an interview that he regretted the need for so much negative advertising. "But we had to break through her aura," he said.

Outspending Fenwick, particularly on TV, Bell had tightened the race. His camp claims their final poll, a week ago, showed him only 8 points down and still climbing. A Fenwick strategist said the margin in her poll was 10 to 18 points, depending on turnout.

Fenwick has a bigger phone canvass going, but she has been put somewhat on the defensive by Bell's attacks. Her first wave of TV spots featured celebrity and constituent praise. The gracious lady in the ads said nothing more controversial than "So nice to see you" (to an elderly constituent) and "God bless you" (to a child).

She says she is a real Reaganite because she supports tax and budget cuts, and denies she is against a strong defense or ever opposed the death penalty "as matter of principle."

Left to her own instincts, Fenwick says, she would go much further in rebutting what she insists are "gross misrepresentations" of her record. Her managers have kept the combative streak she has shown in House debate under tight restraint, but she manages to slip the leash now and then.

When Bell accused her in the Glassboro debate of co-sponsoring "the Kennedy nuclear freeze," Fenwick shot back, "I have nothing to do with that. My opponent should know that is in the Senate. I support the [Silvio] Conte Republican resolution in the House."

It is the same resolution.

Most of all, Fenwick reminds every audience that she has never lost an election for the state assembly or the House, while Bell was beaten by a Democrat last time out.