Grandmother Miller, a Scotswoman weary of family responsibilities, set off on a vacation trek that would give most Americans her age screaming nightmares--a trip on her bicycle, the sturdy ""Daisy,"" from Virginia to Oregon. Along the way, her jaunty chronicle offers views of our wide open spaces and elegant-to-ramshackle byways. Not entirely a headlong adventurer, Mrs. Miller put up at an occasional motel, camped as much as possible near habitations (with permission), and accepted lifts--after a muscle-popping pump in a Kansas windstorm, riding joyfully on a bus, iced beer and burger in hand. Virginia was horse country--but hard chips, instead of hay, made rough bedding; and later she was joined in her tiny tent by a bounce of poor black children whose family had given generously of their meager fare. In Kentucky she saw the aftermath of a devastating flood in rural hill country, and helped out by subbing as a roadhouse dishwasher and sorting a druggist's damaged stock. Lonely in Kansas City, she expediently joined a welcoming AA group. And she disliked the plastic unreality of Salt Lake City. There was sometimes real danger: mountain sickness in the Rockies (""precipitous, bleak and very forbidding""); near-strangulation by Daisy's lock cord when she thought the bike was being stolen; and a frightening snowstorm in Idaho, where she was rescued just in time. Staying in motley accommodations, meeting all sorts, Mrs. Miller resists the temptation to draw conclusions about the national character, only wondering about such things as the width of our main streets, suburban lawns instead of gardens, and the staggering amount we spend eating out. In all, a pleasant uncurling of a narrow ribbon of trans-travel across the continent by a bright, properly considerate, and sprightly lady.