What I do is immediately release the pressure on the bulb after I pull it out of the water and then invert the pipette as air lifts the water up into the bulb. I use the same method you do to get the water into it intially.
The biggest problem I had with this kit is getting all of the air bubbles out of the syringe when pulling titrant out of the bottle. What I do now is to leave that small amount of titrant in the tip of the syringe after a test and then cap it tightly with the syringe cap. The next time I use it, I just dip it in the titrant bottle and pull up. Voila! No more air bubbles!