The phrase "bear with composure" conveys a sense of calmness and ability to handle difficult situations. Some synonyms for this phrase could include "remain composed", "maintain one's cool", "stay patient", "keep one's composure", and "stay calm". These words all express a similar sentiment of being able to handle stress and maintain a level head in challenging circumstances. Other related words might include "persevere", "endure", or "sustain", as each of these implies a sense of staying steadfast in the face of adversity. Ultimately, using any of these synonyms can help to convey a sense of resilience and strength amidst challenges.