Is "bump into their conversation" a correct sentence to express getting into others conversation unexpectedly?

Solution 1:

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barge into (TFD)

  1. To abruptly and/or rudely interrupt or intrude on someone or something without warning.

as in:

My bedroom is a private place, you can't just barge in like that!

John thought he'd found the door to the restroom, but he accidentally barged into the board meeting instead.