Bittinger attended the Massachusetts Institute of Technology, Cambridge, from 1897 to 1899, but left before taking a degree in order to pursue artistic training. His enrollment at the New York Art Students League probably predates his years of European study. Bittinger was in Paris at the turn of the century, where he attended the Ecole des Beaux-Arts from 1901 to 1905. He also studied at the Sorbonne, as well as the Colarossi and Delecluse academies during his Parisian years.
Bittinger joined the United States Navy in 1917, rising from Machinest's Mate to the rank of Captain; he was stationed in Rochester, New York, where he became a specialist in the science of color, working in ship camoflage. Following his service in World War I, Bittinger returned to Washington, D. C., which remained his winter home until his death. After 1929, however, he spent the warmer months at his home in Duxbury, Massachusetts, where he taught painting and founded the Art Association. Bittinger was also associated with the artists colony at Old Lyme, Connecticut.
Bittinger's work was first represented in an Academy annual exhibition in 1907. Two years later the Academy awarded him a Hallgarten prize, and in 1912--the year of his election to membership--the Clarke prize. He remained a consistant participant in Academy exhibitions through 1938, the year following his elevation to Academician.
During World War II, Bittinger served as Chief of the Camouflage Section for the Bureau of Ships, United States Naval Reserve. Additionally, he was a member of the National Geographic Expedition to Canton Island, and painted various aspects of the atom bomb experiments at Bikini Island in 1946. Bittinger demonstrated this extraordinary experience with a final, and uncharacteristic, submission to an Academy annual, First Bomb at Bikini, shown in the 1949 exhibition.
Although Bittinger executed portraits of persons, he became especially known for his carefully studied, detailed portraits of historically important or well recognized room interiors. For example, he painted the blue room of the White House, and the libraries of the New York University Club and the Boston Atheneum.