His work is concerned with landscape and mythology, but he also composed portraits. He is best known for his illustrations of early editions of Bland tomtar och troll (Among Gnomes and Trolls), an anthology of Swedish folklore and fairy tales. Bauer was born and raised in Jönköping. At 16 he moved to Stockholm to study at the Royal Swedish Academy of Arts. While there he received his first commissions to illustrate stories in books and magazines, and met the artist Ester Ellqvist, whom he married in 1906.

Bauer, Ester and their three-year-old son, Bengt, were on their way to their new home in Stockholm, where Bauer hoped for spiritual renewal and a new life for himself and his family. On the night of 19 November 1918, when the steamer left Gränna it was loaded with iron stoves, plowshares, sewing machines and barrels of produce. The weather was bad and by the time the steamer was at sea a full storm was raging; the wind caused the cargo on deck to shift, some of it falling overboard, further destabilizing the ship. The ship capsized and went down, stern first, just 500 metres (1,600 feet) from the next port, Hästholmen, killing all 24 people on board, including the Bauers.