My son bed wetted at that age. He's now 14. I only took that plastic mattress protector off about a year ago. Personally I dont think there is much you can do, apart from not get stressed by it. As long as you've checked out medical reasons and tried common sense ideas, like avoiding drinks at bedtime, I think you will just have to accept it and not make too much of a problem out of it. I'm not sure that going to the gp is a good idea as it might embarrass your son more than he is already. I didnt take mine to the GP, we just lived with it. He didnt wet the bed every night - maybe once a month at that age, and it wasnt a full on soaked bed - just a damp sheet. Basically I just did a lot of laundry. I didnt really say much to him about it because he knew he was doing it and felt bad enough. If he ever mentioned it I just said not to worry about it, lots of boys find it difficult.
I also have two daughters, one of whom was dry at night before she was two and has literally never wet the bed once! - I say that to show that it isnt to do with my poor parenting skills or anything like that. I really think it is just something boys find hard to get the hang of. I'm sure your son will get it soon though.