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After completing her residency at NYU, Bath began a Corneal fellowship program at Columbia University, which focused on corneal transplantation and keratoprosthesis surgery (1973 to 1974). While a fellow, she was recruited by both the UCLA Jules Stein Eye Institute and Charles R. Drew University to co-found an ophthalmology residency program at Martin Luther King, Jr. Hospital. She then began her career in Los Angeles, becoming the first woman ophthalmologist on the faculty at Jules Stein Eye Institute at UCLA. When asked who her mentor was, Bath responded by saying her relationship with family physician Dr. Cecil Marquez inspired her to pursue this specific career. She was appointed assistant chief of the King-Drew-UCLA Ophthalmology Residency Program in 1974, and was appointed chief in 1983.