Bouncing and rising into a punch is a somewhat odd means of delivering a punch, but it is a critically important skill to develop because it eliminates the need to stop movement and plant yourself before firing off a punch. When you plant yourself and cease movement, you are massively telgraphing your intentions and that will clearly undermine your ability to properly launch an offensive attack.

Here is a basic drill:

Stand in front of a bag and do a short squat. As you rise up, punch...but keep yourself from standing up straight. Stay in a hunched boxing position.

There is an advanded version of the above drill where you move repeatedly in a semi-circle around the bag at launch punches smoothly at the right, left and center position of the semi-circle. Again, this should be performed in constant motion while eliminating any unnecessary pauses between shots.