At the end of the first day's ride, with 20 miles down and about 18,000 more to go, Nancy Bertram's legs felt like mush and her seat like someone had spanked her with a hockey stick. Four thousand miles later her legs are fine. But when Bertram rode into Washington last week, she seemed to be riding a bit tall in the saddle.

"I still fantasize about putting a tractor seat on my bike, with a nice soft pillow," said the 23-year-old, who left Denver in May on a two-year, two-wheeled odyssey around the United States to raise money for people who can't walk.

Bertram is earning money by the mile for the Paralyzed Veterans of America, a 36-year-old organization devoted both to helping paralyzed armed forces veterans adjust to their handicap and lobbying society to adjust itself to them.

Working as a nurse for two years in a Colorado hospital that specialized in spinal cord research gave Bertram the desire to help. Challenging herself to an adventure at the same time seemed appropriate.

"I think people are more willing to give when they see that I'm working hard and giving," says Bertram, who hopes to raise more than $20,000 by the end of her trip.

Bertram is tiny, 5-foot-2 1/2 on her tallest day and at 95 pounds, a stone lighter than her 12-speed bicycle with three sets of saddlebags loaded. She rides the highways and byways alone, sleeping in farm fields and parks.

She has ridden through the green hills of Vermont and the bombed-out south Bronx. In small towns she is celebrated. In Philadelphia she was mistaken for a bag lady. And everywhere people are surprised, at times even skeptical, about her seemingly naive enthusiasm.

"When I first met her, when she came blowing in here with all that energy, I said, 'Is this girl for real?' " says Jaime Burrell-Sahl, the treasurer of a local paralyzed veteran's chapter, who was host to Bertram in his Potomac home for a few days while she was in Washington trying to line up more pledges. "Then you realize she is. Everybody falls in love with her."

Burrell-Sahl is paralyzed below the waist as a result of a freak injury during World War II. Actually, the injury occurred two weeks after the Japanese surrendered. But a few kamikaze pilots refused to submit. Burrell-Sahl was 17, celebrating war's end on a submarine tender in the Phillipines, when a plane dove on him.

"It is even more ironic," says Burrell-Sahl, now 55 and laughing at the tragic humor, "I was shot by one of my own shipmates who panicked and fired a machine gun into my station. Five of us were shot. I got knocked from one deck to a lower deck and my spine was broken in three places."

Burrell-Sahl went to college and graduate school to become a psychologist. He worked with the Peace Corps for five years and helped design the selection process for volunteers. In Bertram he sees the same spirit of adventure and altruism that characterized the best of the Peace Corps experience.

Bertram believes in granola and good vibrations. And the first five months of her trip have done nothing to undermine that belief. People have been unfailingly friendly, the weather has been kind and her bicycle has suffered nothing worse than a few flat tires. She has one scar on her knee, but that came from shaving with too sharp a blade.

"A few cows chased me in South Dakota," said Bertram, who has chocolate brown eyes and the wholesome good looks of a college cheerleader. She also has a nice, modest way of looking at her own accomplishments.

"When I started I didn't know anything about bikes, the proper clothing, anything," she said as she packed her bike before setting out for Pittsburgh. "I figured I'd just train on the road. That was very dumb."

Bertram's trip has taken her from Colorado north through South Dakota and Minnesota then across the top part of the country to Maine with a jag into Canada. She rode down the east coast into Washington, with urban stops in the Bronx and Philadelphia. Her longest ride was 150 miles one day in Michigan, and she averages about 80 a day.

She has learned to live like a hobo and dream about hot baths. She will ride through rain, but a pretty lake will stop her cold. And she has learned nice things about herself.

"I'm amazed at how much I can push, push, push," said Bertram, climbing softly into the saddle. "You just set your teeth and go."