Bagel took an interest in painting from a young age and took evening classes at the Vilnius Academy of Arts. He joined the Yung-Vilne group, which was formed by young artists, Yiddish writers, and poets from Vilnius, and he contributed to the exhibitions organized by the group. In 1927, he left for Germany where he joined the Bauhaus arts and architecture school in Dessau. From 1928 to 1932, he studied under Paul Klee, Wassily Kandinsky, and Lyonel Feininger. His painting was then very close to abstract art. He later maintained close bonds with former students of the Bauhaus school who lived in Paris: Joseph Weinfeld, Jean Leppien, and Gitel Gold, who he married in 1932, with whom he had a son Amos.

Bagel settled in Paris in 1933, illustrated children’s books for the publisher Nouvelle Revue Française and worked on photographic reports for the VU agency.

In 1939, he enlisted in the French army. He was discharged from service, and worked for an architect in Toulouse during the Occupation. He was involved in the Résistance making fake documents.

After the Liberation, Bagel returned to Paris and illustrated numerous Yiddish journals, such as Presse Nouvelle (New Press), Droit et Liberté (Law and Freedom), La Semaine Juive (The Jewish Week), A Nouveau (Once Again). He also illustrated several books including Montre by Sholem Aleichem. He also produced theater sets and costumes for the Yiddish art theater company YIKUM.

From 1947 to 1968, he ran the Twentieth Century Fox design studio. At the same time, he lectured on painting. In 1959, for the centenery of Sholem Aleichem’s birth, UNESCO commissioned him to create a series of fifteen large paintings inspired by the Yiddish writer’s work. After exhibiting his work at UNESCO in Paris, he gave it to the Sholem Aleichem foundation in Tel Aviv.

From 1945 to his death, Bagel was involved in the journal Architecture d’aujourd’hui (Architecture Today).