The phrase "burst out with" is often used to describe a sudden and often loud expression of a thought or emotion. However, there are many synonyms that can be used in place of this phrase such as "erupted", "exploded", "blurted out", "spewed", "released", "spit out", "sputtered", and "let out". Each of these synonyms has its own subtle nuance, and which one you choose to use will depend on the context of the sentence and the tone you want to convey. Regardless of which synonym you choose to use, they all convey a sense of sudden and unrestrained expression of thoughts and emotions.