“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.
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.