(This assumes you already know something about doing animations in Bryce.) Use the animation controls inside the Materials editor (at the bottom). Set a key frame at the last point where it should appear solid, then go to the frame where you want it totally transparent, and change the materials so it's invisible, and set another key frame. As Bryce generates intermediate frames between the two key frames, it will change the materials, a bit at a time, so the object goes from fully visible to fully invisible.