"Bit the bullet" is a common idiom that refers to the act of facing and enduring a difficult situation, often with courage. If you're looking for synonyms for this phrase, you can consider "gritted one's teeth", which means to endure a situation with determination and resolve. Alternatively, you can use "took the plunge", which means to make a bold decision and act on it despite potential risks or obstacles. Another option is "faced the music", which means to confront the consequences of one's actions or decisions. These synonyms can add variety and depth to your writing, and help you convey your message more effectively.