“We all busted out laughing.”
You're telling a story about a funny mistake that your friend made. You've just described the mistake, so now you describe your reaction.
We all busted out laughing.
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The phrase "bust out laughing" describes someone suddenly laughing really hard. You "bust out laughing" when something funny and unexpected happens.
This is a casual and slangy spoken English phrase. The more correct expression is "burst out laughing":
They all burst out laughing at the sight of Emmett in his gorilla costume.
Use "burst out laughing" in more formal and written English.