A word that describes a liquid's tendency to form bubbles

You could rightfully say that the mouthwash has a lower surface tension, or that it is a better surfactant (or tensioactive). It may not sound fancy, but at least it will be physically correct.

The point is whether the bubbling has to be triggered somehow (e.g. by gargling) or not. A frothy, foamy or fizzy liquid is one that gives off bubbles spontaneously, while mouthwash or soap are not foamy as long as they're not shaken.

Foaming tendency

This term appears utilized in industry where material properties are critical for function. (http://www.astm.org/Standards/D892.htm)

For the first replacement:

I don't like this mouthwash. Bubbles foam out when I gurgle, because it has a higher foaming tendency.

Second one requires some shoe-horning to get it to fit the sentence.

I don't like this mouthwash. Bubbles foam out when I gurgle, because it's more likely to foam.

Reworded

I don't like this mouthwash. Bubbles foam out when I gurgle, because it has a higher tendency to foam.