The fine art of winning a federal contract traditionally has featured high-pressured lobbying, three-martini lunches and years of nuts-and-bolts experience.

And then there is Jane Y. Shaffer of Heath, Ohio.

Shaffer, the family tour director for an electrical plant in Columbus, won $31,690 from the Department of Energy in the form of a grant to produce a cartoon bingo game for elementary school children.

She did it with luck, a two-year-old idea that Walt Disney Productions had turned down and a form that almost ended up in the wastebasket.

Last April, Shaffer's husband, Marvin, sent away to DOE for a grant application to build a windmill for his back yard. When the form came, Marvin Shaffer realized he couldn't qualify, and he threw it aside in disgust.

Jane Shaffer found it a few days later and, on a whim, submitted her two-year-old idea for teaching children how to save energy.

Her "Energy Bee" bingo game included 34 cartoons that teachers would show their class, letting the students match them on cards. She envisioned slogans and rhymes for her cartoons such as: "Jack Rabbit starts and stops wastes a lot of gas," or "If only going a block or two, ask mom and dad to walk with you."

Her husband and friends told her she was wasting her time because there were so many other "serious" applicants. But last August, DOE's Region V office in Chicago awarded 50 grants, worth $1.3 million, in the Midwest. Shaffer's was one of them.

"She was in competition with hundreds of other applicants," said Roberta Dalton, a program manager in Chicago. "This grant got no special attention."

In return for its $31,690, DOE has given Jane Shaffer a year to produce her game. But it has no plans to put it in the classroom.

"Usually, these projects have a final report written up, and they are sent to the Oak Ridge Technical Information Center," said Thomas Katisch, DOE's Chicago office program director.

The Appropriate Technology Program grants are designed to help individuals or small businesses develop new ideas, while letting them retain the marketing rights. The administration proposed to "zero-fund" it for fiscal 1982, but Congress has kept it alive with a $2.88 million appropriation.

"If we can get some juices flowing to get a product on the market," said DOE spokesman Brian Quirk, "then we've been successful."

When told of DOE's plans, or lack of them, for her game, Shaffer said she would try to market it through teachers' magazines.

"It's a shame that they don't do more for this age group," she said. "The kids are so impressionable."