Switching to a short-scale bass is a good or bad idea?
(Yes, Bill played short-scale basses, but it's another topic)
Trying in a music shop does not gives an idea on the long run... Less demanding for the left hand, and lighter to carry... But the strings are maybe too loose for the right hand, hence you may be lost if accustomed to a big Fender P.

it is fun to play a short scale bass. and generally its a lighter instrument. If you're used to old standard basses like Precisions, etc, playing a short-scale bass will be a nice break, and the sound is pluckier.

bigger effect is probably getting the right strings for the sound you want.

I like flatwounds, I suspect Bill also played (plays) flatwound strings.. a rootsier sound generally.