Often suggests sadness or difficulty around ending a close relationship or marriage. Their decision to bust up was tough on both of them.
Pro Tip 2/3
Casual Speak
Used in casual conversation, usually not in formal situations. I heard that they're going to bust up soon.
Pro Tip 3/3
Colloquial Variation
'Bust up' is less formal than 'separate' or 'divorce,' and may not imply legal action. They're not divorcing yet, just busting up to see how things go.