What are the white bulb like things on my transplanted eyebrow after contact with water?

Great question! Some of the white "pulp" that you are seeing is the epidermal cuff of the follicular unit.  Don't worry, this is normal.  As your grafts heal with continued care, you will this epidermal cuff shed.  It may take a full week, sometimes ten days. I tend to tell my patients just to leave the follicles alone when I'm doing facial hair transplants.  But I would tell you the best thing to do right now is follow the instructions your surgeon has given you.  Congratulations on your procedure! Best of luck healing! 

The white bumps are typical following washing of the grafts this many days out.  They are the residual skin tag/scab of the placed graft and will be shed in the next 5 to 7 days.  Washing the grafts with water removes any residual blood around the graft and moistens the scabbing around it producing a white appearance.  Whoever performed your surgery did an excellent job and you should have great longterm results.

These white spots are the skin edge of the graft taking on water and that is why when it is dry, it goes away. I always trip off the skin of my grafts to avoid this and other problems

This is normal and expected. It will take 7-10 days for everything to be completely healed but at 4 days it is already looking pretty good.