What is the scientific term to describe the operation of a bong?
I think the term describing the initial process of separation of the solid phase (dust particles) from the gas phase via bubbling is a wet scrubbing process.

On an industrial scale, it's more efficient to spray liquid phase, whereas on a laboratory scale bubbling in a compact glass gas scrubber or a gas washing bottle is more convenient.
In order to increase efficiency of the lab apparatus, it's preferred to


keep the surface between gas bubbles and liquid phase as large as possible;
increase time of contact.


This is usually achieved by producing many smaller bubbles by using a spiral tubing (larger particles), frit of long columns filled with Raschig rings.




Figure 1. Left: Büchi miniScrubber, a glass gas scrubber (Source: Büchiglas — Gas scrubber). Right: Corning PYREX® 125mL Gas Washing Bottle with Extra Coarse Fritted Disc (Source: Thomas Scientific) 

Eventually collected insoluble dust particles tend to settle out from the solution; this a basis for sedimentation, another separation technique.