There where P bass specific cases made during the American Series years (2000-'07) ... they were the bass shaped case, not rectangular ... there were actually two different versions of this case, the one used the first couple years had a more of a 'pebble' finish with the outline of a bass body on the top, and the other was very smooth finish, with just the word Fender on the top ... the pebble finish had 2 straps to hold the top when open, the smooth finish only had one .. interestingly enough, at least the earliest versions of these also actually had the mould cut to even fit the elongated upper horn of an '89-94 Longhorn bass ... I think that would have been a hold over from the Fender 'Red Label' cases ...
All the rectangular cases that I have seen Fender use fit both a P and a J ... when I have used a P, I just rolled up a small towel at the body end to help secure it ...