Bye-bye bones are very special in that they are highly desirable (usually edible), long-lasting pacifiers that your dog gets only when you leave the house. They are typically used for dogs who get nervous or anxious when their owners leave. The idea is to have the dog associate the person's leaving with something "outta this world" great so that the anxiety is overrun by the goodness of the bone. The "bye-bye bone" doesn't have to be an actual bone, but it can be if that's what gets your dog drooling. Here are some good examples of BBB's:

Knucklebone- lasts long, tastes extra-good.

A marrow bone, pre-filled or filled by you with peanut butter, then frozen.

The all purpose kong toy-put the most valued stuff in first, then plug up with a biscuit or something, so the dog must get through it to get to the good stuff. You have to stuff the kong well enough to make it difficult for the dog to unstuff it, but not so difficult that the dog gives up.

Remember to take the BBB away as soon as you get home! He only gets access to it when you are leaving!!