First things first: When we talk about a dry cappuccino, the word "dry" is describing the flavor profile. It is not an description of what the milk froth should be. Cappuccino foam should always be smooth and wet, and well incorporated into the whole of the beverage.
A dry cappuccino is simply calling for a greater ratio of foam to milk. This leaves the espresso less dilluted with milk, giving it a stronger flavor and a fuller, deeper presentation of the coffee roast, leaving dry tones on the palate.
The proliferation of the "Bubble Bath Cappuccino" is sad to see. When someone who is used to that sort of presentation sees a proper cappuccino, he or she is usually a little confused. After all, even a well-made dry cappuccino can approach the look of a latte, and leave a customer skeptical. The foam is there, it is just very smooth and practically indistinguishable from the pure liquid of the milk. This is because the aeration of the milk created during the stretching process on the steam wand should be developed throughout the milk, not just the top. That is the importance of rolling and swirling the milk, and what gives it that heavenly texture.
And trust me... after enjoying a cappuccino poured without a trace of visible bubbles in the milk--giving it a glossy sheen, and leaving it, desirably, with no great sculpting properities to speak of--it will be hard to ever again drink a tall, frothy mess passing as a cappuccino in this city.