I shower when my port is accessed as well, it is covered with tagaderm, and the tail (as I call it) always hangs down (my port is located on my left, below my breast about 2-3 inches). It only gets wet underneath sometimes if I have sweat a lot and the tagaderm loosens. I change the dressing/tagaderm myself if it starts to come off. I do try to keep from standing under the direct flow of water when showering. But if I couldn't shower for two-three weeks, I would feel gross.
The reason I mention the tail hanging down is so that the water can't flow in along the tube. I also like it consistent so it is comfortable when I do my vest.
I used to cover it with saran wrap taped to my skin, but I quit that after a couple years. I have had a port for 10 years, this is my second one. I love it.