This has been an on going problem since replacing my exhaust pipe and muffler. At first some family members as well as a mechanic told me it was the transmission making this noise. I took it to a transmission shop and he told me nothing was wrong with the trans and that it shifted well. He put the car on the lift and started taping around and when he hit the cat the noise was similar to the noise I was hearing. BTW he drove a 87-91 Bonneville too and he loved his car so he definitely knew about the Bonneville trans.
So fast forward, I changed my oil and after pulling the car off the ramps, the noise stopped as if the piece of *to be determine* had fallen back and this has lasted until last Friday. The noise is back and the sound has changed. It only makes the noise when I'm in Drive and when I'm holding the brake pedal. You will notice in the video when I put the car in park the noise stops. Also when I'm driving I don't here the noise. It also robbing my horsepower a little. I believe it may be the cat.