Hmmm...sounds like what you're looking for is essentially an inline monitor with a pass-through for the signal and a monitor jack...or a preamp with a monitor jack that sends the amplified signal on to the amp.
#2 sounds more likely to me - there's not that much signal coming out of a bass jack, and there needs to be a reason to put electronics in the signal path. A preamp would be one reason to put a device in the signal chain.
But wait!....that might also be something you'd find in a wireless setup - the transmitter might have a headphone jack.
B&H Photo has a number of wireless systems ranging from $75 up...it also strikes me that using a wireless headphone might let you tune into the frequency that's being used to send the signal.
One possibility is this - the specs mention that you can send the signal to specific wireless headphones: "The audio signal can also be sent to Wi Digital System's optional Wi Studio-M digital wireless headphones, model JM-WHM01, for a high quality wireless monitoring experience."
http://www.bhphotovideo.com/c/product/766504-REG/Jangus_JM_WAL35_Wi_AudioLink_Professional_Stereo.htmlI only spent a couple of minutes reading this, but if the price tag fits, it might be worth studying.