The topic of "fast bass" tends to polarise opinions. There are two main camps here. In one, "fast bass" is a myth that doesn't exist. They reject the use of the term completely. This is an objectivist opinion. In the other, the term is accepted as a subjective one meaning "tight and accurate bass." It would be helpful if the audio community could agree on this so that we can stop arguing over the meaning of a term, or if it even exists!
Taking it literally ...
Out of interest, let's first explore a literal interpretation of the term. Let's see how fast bass really is, as measured by the speed of cone travel. What is the fastest bass we can get, as measured by the speed of cone travel. First we'll take a 6.5" midbass driver and play it at a level that audiophiles will use in a room to get "fast bass." We'll play it at a moderate level of 70db at a distance of 4m and we'll see how fast the cone moves at 60 Hz. We'll use the classic Scan Speak 6.5" midbass - 18w8545, which is a fairly expensive midbass used in many high end designs. We need 0.4w to achieve this level and the cone excursion is a mere 1mm from peak to peak. What is the speed involved? The average speed considers distance and time.
Distance is 1/1000m and time is 1/60 sec. So that is 0.001 metres in 0.016 seconds (16ms). So we have 0.06 m/s or 0.2 km/h. The average person walks 25 x faster! If we want the cone to move faster, we could turn up the volume. If we use 4x as much power, we get twice the excursion and twice the speed, but we all know that everything goes backwards from there.
What happens if we use a subwoofer? If we use the Exodus Tempest-X, which is a 15" driver and compare at the same spot with identical output, the cone moves one third as much due to it's size. It is even slower. But we want to get some speed here so we feed it 2kw of power and the excursion is now 28mm - so the speed is 28x as much. Now we've sped up to the speed of a person walking at last, but we can hardly call this fast! Let's rule out velocity as being relevant to "fast bass."
What should we do with this term "fast bass?"
We have a dictionary to define what words mean, so that we can all communicate without debating what words mean - we can get on with life. In technical fields certain terms are defined and generally accepted due to practical need. There is a need to agree on commonly used terms so that we don't get caught up in arguing over words, and get on with the discussion. I suggest the best solution is to simply accept the term "fast bass" in the way it is usually intended - as a subjective term that simply means "accurate bass." I personally don't use the term, as it becomes something of a red herring and often derails discussion. It's much easier to say "accurate." But if someone uses the term fast bass, I know what they mean. We can debate what actually constitutes fast bass, and how to achieve it, but I wish we could at least agree on the term itself!