Bada Bing Gentlemen's Club Basic Lighter

“Bada bing bada boom” appeared in a 1958 film The Italian Wedding, where comedian Pat Cooper mentions the phrase.  It has become a Brooklynesque slang phrase used in a fashion that the speaker presumes the listener knows the course events will take, and skips the details to a conclusion.

It is associated with mob figures , who use it to imply that something is concluded.
The phrases origins are accredited to comedian Pat Cooper, who is known for his  “Brooklynisms” such as “fuhgeddaboudit”.