When someone barges into a room uninvited or speaks up without being asked, we often use the term "bursting in." This phrase implies a sense of urgency, aggression, or rude behavior. However, there are several antonyms for "bursting in" that convey a more polite, respectful, or patient approach. These could include knocking and waiting for a response, entering discreetly, seeking permission to speak or enter, waiting for a natural break in conversation, or offering assistance or support in a non-intrusive manner. Choosing the right antonym for "bursting in" depends on the context and the desired tone of the interaction.