A student of the German botanists Julius von Sachs at the University of Würzburg (1877–78) and Anton de Bary at the University of Strasbourg (now in France; 1879), Bower was associated with the British biologist Thomas Huxley as an assistant and instructor of botany at the University of London (1880–85). He spent most of his career as professor of botany at the University of Glasgow (1885–1925).

Bower postulated that a regular pattern of alternation of generations was established independently in primitive land plants through the evolutionary development, or interpolation, of the sporophyte growing from the zygote following fusion of gametes (sex cells). He believed that land plants developed through the progressive sterilization in the sporophyte of all but a few potential spores to form vegetative cells characteristic of an independent plant.

The precise algal origin of land plants has yet to be ascertained, but questions raised by Bower's work, summarized in his classic The Origin of a Land Flora (1908), have done much to coordinate paleobotany and plant morphology in a widespread study of plant evolution. Bower also wrote The Ferns, 3 vol. (1923–28), Size and Form in Plants (1930), and Primitive Land Plants (1935).