He studied under Matthaei in Dresden and completed his art education with a visit to Italy in 1827-1829.
He was made a Professor at the Dresden Academy of Fine Arts in 1840. Bähr was in demand as a portraitist, and also painted some historical works. He wrote several books: Die Gräber der Liven (1850), a report on some archaeological excavations in Livonia which he undertook in 1846.
Lectures on Dante"s Divine Comedy (1853).
Lectures on the Colour Theories of Newton and Goethe (1863) and The Dynamic Circle (1860-1868), a scientific work which occupied him almost exclusively for the last ten years of his life. Bähr"s large collection of Latvian medieval antiquities was purchased by the British Museum in 1852.
He died at Dresden on 29 September 1869.