What factors influence the maximum speed of an airship?
I'll do this without most of the math since your target audience won't want to read equations in your story.

In the simplest terms, the maximum speed of an airship occurs when the maximum thrust generated by its engines is equal to the drag it experiences while being pushed through the air at that speed. That drag depends on the diameter and length of the airship (more specifically, the projected frontal area and the total "wetted area" of the entire vehicle's outer skin). 

This is a complicated business because the relationships between all of those variables are strongly nonlinear- for example, the drag varies with the speed squared and the power required at a given speed varies with the cube of the speed. 

So in your story: doubling the power of the engines will increase the airship speed only slightly, at the cost of doubling the fuel burn rate and therefore the fuel tank capacity- and thereby reducing the useful payload. 

Similarly, doubling the length of the airship will roughly double the wetted-area drag, which means you have to double the horsepower of the engines or their number in order to achieve the same maximum airspeed as the shorter airship.