Those who believe bulk interferes with speed are missing out a lot especially if they avoid resistance training. The primary source of confusion behind bulk and speed originates from the confusion between power and strength.
Martial arts revolves around power from physics stand point.
What is power?
Power includes your ability to move a load (force) over a distance (point a to point b) within a certain time (one second).
In a high kick to the head, the force is your foot and your leg. The distance is from your foot to your opponents head. The time is how fast you can do it.
When you practice moving heavier loads over the same distance, your strength which is the ability to move weights increases.
When you practice moving heavier loads and do it faster, your power increases.
Adding wrist and ankle weights during practicing your punches and kicks is one way, not necessarily a safe way, to increase your strength and power.
Try to punch faster without the additional load and you limit how much your power increases.
Increasing power may or not add bulk as in muscle mass. Adding muscle mass requires specific type training that only in part is power related.
Comprehensive martial arts training includes power training even when the motions of the art do not directly associate with the motions within the power training. Remember not to go too far in the way you power train and the way you fight. Practice the way you fight or compete.
For example, as a grappler practice pulling power, as puncher practice plyo pushups.