From the pictures and dimensions of the Bart 5 string P set it doesn't look like they are a short/long coil like that Squier 5 String
The Jazz will work just fine.
I was able to get an Aguilar OBP 2 In a factory Jazz rout, but I had to rout a cavity under the pick guard for the battery. Its a very tight fit, If I were to do it again I would have routed the cavity big enough for the battery and pre.
S.U.B. Club # 29
GK Club # 750
Texas Bassist Club # 164