Why did bacteria vanish from science for over a century after their discovery?

Because they were barely visible even to the one man who had seen them, and he kept his secret. Bacteria were first observed by the Dutch microscopist Antonie van Leeuwenhoek in 1676, using a single-lens microscope of his own design, and their size was just at the limit of what his simple lenses could resolve. He never revealed how he made those lenses: his exact method remained unknown for centuries. By the end of the 17th century he had a virtual monopoly on microscopic discovery, and his contemporary Robert Hooke complained that the whole field rested on one man's shoulders.

Leeuwenhoek wasn't a trained scientist. He ran a draper's shop and wanted to inspect the quality of thread better than the magnifying lenses of his day allowed. He made more than 500 lenses, and his surviving microscopes magnify up to 275 times. He didn't even realize he had found a distinct kind of life: he called every tiny creature he saw, bacteria included, an "animalcule," and described them in letters to the Royal Society of London. Then, in one of the most striking gaps in the history of science, no one else saw bacteria again for over a century.

The word "bacterium" itself came only in 1828, from the naturalist Christian Gottfried Ehrenberg. From there the field moved fast. In 1859, Louis Pasteur showed that the growth of microorganisms causes fermentation, and with his contemporary Robert Koch he became an early champion of the germ theory of disease. Koch finally proved that theory through his research on tuberculosis, earning a Nobel Prize in 1905.

Today bacteria are known to be everywhere, among the first life forms to appear on Earth, and each of us carries roughly 10 trillion to 100 trillion of them, mostly in the gut. Most are harmless or kept in check by the immune system, and many are beneficial.