Mistwell
Crusty Old Meatwad
This is, of course, how 3rd edition wound up with different categories of bonus - enhancement bonus, natural armor bonus, luck bonus - that everyone complained about so much and forced them to fix.
I would think that the ultimate intent is to fix it that any bonuses don't stack with each other, but I'm not sure how that could work. I guess you could start by saying that +1 armor doesn't give you a +1 magical bonus to AC, but is simply AC +9 instead of AC +8.
"Magical bonuses do not stack with each other" is the easiest way to solve this issue. So if you have +1 armor, +1 ring of protection, +2 from barkskin, and +2 from haste...you have a total of +2 and that's it. It's simple, and works.