Bayer apprenticed under the artist Georg Schmidthammer in Linz. Leaving the workshop to study at the Darmstadt Artists' Colony, he became interested in Walter Gropius's Bauhaus manifesto. After Bayer had studied for four years at the Bauhaus under such teachers as Wassily Kandinsky and László Moholy-Nagy, Gropius appointed Bayer director of printing and advertising.

In the spirit of reductive minimalism, Bayer developed a crisp visual style and adopted use of all-lowercase, sans serif typefaces for most Bauhaus publications. Bayer is one of several typographers of the period including Kurt Schwitters and Jan Tschichold who experimented with the creation of a simplified more phonetic-based alphabet. Bayer designed the 1925 geometric sans-serif typeface called universal,[1] now issued in digital form as Bayer Universal.[2] The design also inspired ITC Bauhaus and Architype Bayer, which bears comparison with the stylistically related typeface Architype Schwitters.

In 1928, Bayer left the Bauhaus to become art director of Vogue magazine's Berlin office. He remained in Germany far later than most other progressives. In 1936 he designed a brochure for the Deutschland Ausstellung, an exhibition for tourists in Berlin during the 1936 Olympic Games - the brochure celebrated life in the Third Reich, and the authority of Hitler. However, in 1937, works of Bayer's were included in the Nazi propaganda exhibition "Degenerate Art", upon which he left Germany in 1938 to settle in New York City where he had a long and distinguished career in nearly every aspect of the graphic arts. In 1944 Bayer married Joella Syrara Haweis, the daughter of poet Mina Loy.

In 1946 the Bayers relocated. Hired by industrialist and visionary Walter Paepcke, Bayer moved to Aspen, Colorado as Paepcke promoted skiing as a popular sport. Bayer's architectural work in the town included co-designing the Aspen Institute and restoring the Wheeler Opera House, but his production of promotional posters identified skiing with wit, excitement, and glamour.

In 1959, he designed his "fonetik alfabet", a phonetic alphabet, for English. It was sans-serif and without capital letters. He had special symbols for the endings -ed, -ory, -ing, and -ion, as well as the digraphs "ch", "sh", and "ng". An underline indicated the doubling of a consonant in traditional orthography.

While living in Aspen, Bayer had a chance meeting with the eccentric oilman, outdoorsman and (to those who knew him) visionary ecologist, Robert O. Anderson. When Anderson saw the ultra-modern, Bauhaus-inspired home that Bayer had designed & built in Aspen, he walked up to the front door and introduced himself. It was the beginning of a life-long friendship between the two men and instigated Anderson's insatiable passion for compulsively collecting contemporary art.

With Anderson's eventual formation of the Atlantic Richfield Company, and as his personal art collection quickly overflowed out of his New Mexico ranch and other homes, ARCO soon held the unique distinction of possessing the world's largest corporate Art Collection, under the critical eye and sharp direction of Bayer as Arco's Design Consultant.

Overseeing acquisitions from within Arco Plaza, the newly-built twin 51 story office towers in Los Angeles, Bayer was also responsible for the Arco logo and designing all corporate "branding" related to the company. Prior to the completion of Arco Plaza, Anderson commissioned Bayer to design a monumental sculpture-fountain to be installed between the dark green granite towers. Double Ascension still stands between the twin skyscrapers to this day.

Under Bayer's and Corporate Art Curator Leila Mehle's direction & supervision, Arco's Collection grew to nearly 30,000 Artworks nationwide. Arco's collection was quite eclectic, and consisted of an extremely wide range of media & styles; ranging from large resin sculptures by Dewain Valentine to original signed photographs by Ansel Adams. The vast majority of the collection consisted of original "signed" prints & "artist's proofs" of hand-pulled prints. Major works were reserved for lobbies, reception areas and executive & upper management offices.

Bayer and Ms. Mehle instigated a unique program for the collection in that large paintings and sculptures were often "circulated" within the company and transported from one Arco building to another, often making the journey from LA to New York and back again.

With the purchase of Anaconda Copper, Arco built an office tower in downtown Denver, and again, Anderson commissioned Bayer to oversee Anaconda's Art Collection for the new company. Eventually, Bayer gave the Denver Art Museum a collection of around 8,000 of his works.

Bayer's works appear in prominent public and private collections including the MIT List Visual Arts Center.