2 things.
1. I hope you do realise that there's a lot more to grounding than just lining your cavity with copper foil. In fact, doing just that without anything else will achieve pretty much... nothing.
2. It's not meant to change the tone of your bass. It's meant to minimize the 60cycle hum you get from single coil basses, or poorly shielded/wired/grounded basses.
Your BBN5A has humcancelling pickups - so even with a good grounding job, the difference before and after shielding that bass wouldn't be that significant as compared to doing the same thing with a jazz bass.