If your into true BB'ing than you train for the pump, the whole object of training. Keeping the pump with-in an area as long as you need. A pump is just a congestion of blood trapped in one area, which never means lasting muscle gains. In your case, the arms. May consider a full pump a false positive.
If you do cardio right after a pump workout the blood will naturally be required in other parts of the whole body. So the pump in the arms will deflate and becomes 'soft' (there is a penis/hard on joke here that could be said). Lesson learned here is do not do cardio right after a serious BB'ing workout. Or on the same day, for that matter. If desiring cardio on a BB'ing training day, than do some light work before the weight work. Or wait 4 hours, or so,after for the cardio phase to start. Good Luck
Side Bar: Most try for too much of a pump, working for that false positive again. It's like having a empty glass under a running faucet. You can only get so much water into that glass, any more only runs off the sides of the glass. As with this, you can only get so much blood pumped into a muscle area and no more. Doing more sets is wasted effort. Some may find that after 10-12 sets the muscle worked actually reduce some of the pump. The body is telling you something here; enough is enough..