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Modernism is a highly contested area, a "mixed blessing" in typography as elsewhere.
It is possible to clear up one source of the confusion. There is a style of typeface sometimes known as "modern". In the nineteenth century it was "modern", and it is the standard text face in English---from the first quarter of the nineteenth century until the first quarter of the 20th. It is characterised by a strong contrast between thick verticals and thin horizontal strokes, a vertical axis and vertical stressing, little or no calligraphic quality---such as it has related to the steel-nibbed "copperplate" pen not the broad-nib pen---with a much closer kinship to engraving than to writing, thin horizontal serifs, ball terminals on letters such as f and j. As Bringhurst correctly points out it has little to do with "modernism" as a movement in art and philosophy: it is, rather, closely related to "romanticism". Its only, distant, relationship with modernism is that it belongs to the era in which printing was industrialised.
Modernism in typography, as in art, is generally a movement which began around or after World War I, flourishes between the wars, and is then challenged and diluted after World War II, although never fully vanquished. At its best and strongest, modernist typography is marked by a fairly coherent set of aesthetic beliefs: priority is to be given to function (the "decorative" is not beautiful); rational principles (systematic geometry, grids) are essential; there is nothing wrong with the mass-produced, and there is no special value to be attached to the appearance of the "hand of the craftsman"--much less to the false pretense of craftsmanship in items that are in fact a product of the machine.
In typography these principles tended to manifest themselves in such matters as: a preference for "industrial" typefaces (Akzidenz Grotesk, Helvetica) or geometric typefaces (Futura) over types modelled on or aping earlier forms; a preference for sans serif type over type with serifs (since, on one view, a serif is a form of decoration); a preference for "rational" (especially asymmetric) layouts and grids over traditional centered or "artistic" arrangements; a dislike of decoration; a preference for the honestly industrial (standard sizes, ordinary paper) over the crafty or handmade. Typographic modernism flourished in Germany in the 1920s, under the influence of the Bauhaus and through individuals such as Paul Renner and Jan Tschichold, it flourished in Switzerland in the 1950s and 60s. It remains significant to this day, especially in Europe (it was never so influential in America).
It should be stressed that the particular choices described above are not compulsory to modernism, though they are commonly held to some degree by modernists. A modernist could well, however, become convinced that serifs serve a genuine function, and are not merely decorative. If so s/he would cheerfully prefer to use serif text types--but would still be likely to prefer a relatively anonymous common font over something lush or antiquarian. The approach to typography is informed by and works out of a much more general, philosophical, attitude towards design in general and aesthetics in general. Modernism is not a set of tricks, nor a style: it is an attitude.
Or should be. For every philosophical modernist, there is a trick "modernist", who uses modernism simply as a style--as simply another decorative device or style, a matter of fashion rather than conviction. As Tschichold's Die neue Typographie repeatedly demonstrated, modernist devices such as asymmetry, geometric decoration and grids can easily be abused simply to create the illusion of being progressive. This approach too, the bastard child of the mixed blessing that is modernism, is still with us.