What you're describing is what Fender offered from 1966-73. Those are the years that you could have gotten that color with that neck. The original vintage basses with that combo are pricey though, like $4-8K depending on year and condition.. and they don't come up often. You have lots of other options though..
I've seen some Japanese Fender LPB '75 reissues (they are 3-bolt though I think). You could also get a jazz body from various suppliers and finish it LPB. And many of those suppliers make that B&B neck in Rosewood too (like Allparts for instance), and in 4-bolt also.
You could also buy a refinished vintage bass with a rosewood B&B neck for a lot cheaper than an all original, and re-refinish it in LPB (or find one already refinished in LPB, but that may be difficult).
Fender never made any regular production Precisions with a B&B neck until recently. One I can think of is the Classic Series '70s P Bass,
but it has a maple neck with black binding/blocks.
The Custom Shop might already make model with the features you want, I'm not sure. But you can see what they have on their website. I'm sure they'll do custom orders for anything you want also, if you have the dough.