Since it's in a condition that it's acting up, you can do some creative probing to find where the problem is. Use a non-coductive probe, like wood or plastic, to very lighty tap on the connections, starting right at the pickup connector for the bass pickup. If you use your finger, you will introduce hum and that won't be helpful. Nothing in the cavity is high voltage, so it's safe for probing. Make sure you use a light touch, and then report back where you find you can trigger the pop - it should take much less force to initiate it at the source than when you tap on the body to make it happen.
It's possible that the coax connector for the pickup to look plugged in correctly even when it's not. It's a delicate connector, so if anyone has every gone inside your bass and reconnected this part, it can bend it a little if they are not careful.
