While I dont relate to the "Rainbow Bridge" theory, I can certainly relate to the loss of a pet one has for a very long period of time.
It's amazing how much companionship and love a person receives from having a pet. I just lost my cat, "Miss Peanut" a few weeks ago who was just a few months shy of 14, I lost another who was almost 20, and another who was indeed 20. There's such an empty place in the house without them...both physically and emotionally.
So I wanted to say that I understand your feelings of loss, and I send my sympathies to you.