I tried different cable although its the same type of a cable. Same thing.No noise (normal amp hiss) without the bass plugged in? Your bass is picking up RFI, you might even try something as simple as a different cable or wireless setup if you can borrow one.
Here is the recording.
Notice how when I touch the strings etc the buzz goes away, but touching the J pickup makes it worse (which I think is normal).
My other bass has humbuckers and it is the same thing.
And yes both basses do not buzz anywhere else.
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@mborn