He was born in Philadelphia, Pennsylvania to Henry and Pauline Waber. Although he started a degree in finance at the University of Pennsylvania, he left school to enroll in the army at the onset of World War II. From 1942 to 1945, Waber served the United States Army as a staff sergeant. Immediately following the end of the war, he returned to his studies at the Philadelphia College of Art. Waber graduated and earned his degree in 1951.

Upon graduation, Waber launched his career as a commercial artist. Soon after, he began illustrating and writing children's books. At the age of 28, Bernard married Ethel Bernstein, and the couple moved to New York City and had three children. When his children were young, Waber worked in the art department of Condé Nast Publications, writing his books at night and on the weekends.

Waber has written numerous children's books about the adventures of animals, including Do You See a Mouse?, Evie and Margie and A Lion Named Shirley Williamson. Waber's Lyle series, started in 1962, is his most well-known set of children's books. In the books, Lyle is a city-dwelling crocodile that lives in a bathtub. Lyle's character brings joy to everyone he meets.

Shortly after the attacks of September 11, 2001, Waber wrote the book Courage. In the book, through various characters, children are taught the meaning of bravery.

Waber now lives in Long Island, New York with his wife and grandchildren.