P Bass Pick and Bridge Cover...Interchangeable?

It might fit...a Jazz cover may have more clearance for it though. But, it may not fit, which is more likely. I personally don't think either jazz or p pickup cover will be too attractive over a bridge. Those BA2's are pretty bulky...

 

from guitarpartsresource.com

but i went on their site just now to get you a link and i don't see it anymore. It was called
OVERSIZED CHROME P BASS ASHTRAY BRIDGE COVER
item # OVSZ-BC

you may want to contact them and see if they have any lying around.

 

The precision pickup cover will fit over the BAII, but it won't cover it completely, and will look pretty wierd with the BAII sticking out the ends.

I think I tried a fender j bass cover with my BAII and it had to sit too far back to work. However, the SX covers that come on their 5 string jazz basses will cover a BAII just fine. It's the one you see here:
http://www.rondomusic.com/sjb75c41ash.html

if I hadn't lost mine I'd sell it too you, but I'm sure there's someone else on TB who has one they will part with. I get the feeling that not too many folks keep the covers on their 5 string jazz basses.

 

If you do that, the BA is going to stick out from underneath. IMO, that would look a bit goofy.