Sometimes the cheaper basses use smaller value caps on the tone pot... this may be the case. A smaller value cap will cut the extreme highs which may not be present in the signal anyway. The Tone is just a treble cut knob, so if you have very little treble in your original AMP tone, then you really aren't gonna be cutting anything with the knob.
suggestion... clip the lead from volume to tone pot... replace volume pot for a 500k. This allows you to use the volume as your tone pot as well as your volume. As the 500K value is letting in the extreme highs from your pickups. The end result is a bright attacking sound at 100%. Roll back just a bit and the brightness dissapears but no volume is lost... roll back a bit more and you start getting this smooth fat bass sound, with minimal volume loss. After that the volume starts doing its job by reducing the volume.
I have done this to every bass i have that isn't active.
Try using a 1 Meg pot as well, which lets in more highs... you will find cool tones experimenting with your electronics...
Try adding a push/push 500k volume and wiring the switch to series/parallel for the P pickup...
another cool trick is to wire up a 250K resistor across the outside legs of the 500K pot which would turn it into a 250K pot.
Connect one end of the resistor to one of the outside legs of the volume pot. Now connect the other end of the resistor to the push/pull switch( a mini toggle switch)... from the other side of the switch connect that to the other outside leg of the volume pot...
What you have here is a switchable 250K/500K volume pot.
Your whole musical world will change when you discover electronics....
JON