The antonyms of "bursting out" could be "holding back," "restraining," "suppressing," "repressing," and "concealing." When a person is holding back, they are refusing to express themselves emotionally, while restraining refers to controlling oneself physically or emotionally. Suppressing suggests preventing or controlling the release of emotions or desires, and repressing involves forcibly holding back one's feelings or impulses. Concealing refers to hiding one's feelings or emotions from others, often by adopting a neutral or emotionless stance. However, it is essential to note that the opposite of "bursting out" should not be understood as a complete absence of expression or emotion but rather as a measured and controlled approach.