Bob, I don't know if our ostomy ever becomes so integral to us that we don't think about it at all. For one, we need to remember to change it every 3 or 4 days. On the other hand, even though in the pre-ostomy days our bladder was clearly part of us, we found ourselves thinking about it every few hours when it clamored for attention.
By and large, I find my ostomy a real blessing and a very good friend. I actually think about my bladder less because of it. No need to get up a few times in the middle of the night because of a sensitive bladder. No need to worry about bathroom stops on every little trip that we take.