what exactly did you want it to do?
have a speaker? microphone? what did you want to pair it with? details are what you need to provide if you want any sort of advice.
if all you wanted is a speaker then i would probably disassemble a bluetooth headset for the bluetooth module and leads going to the speaker. since the earbud speaker might not be loud enough you might have to pair it with a cell phone or home phone speakerphone speaker or something of the sort.
generally you would be scrounging parts from a few different sources.
another alternative idea is just to get a speaker which fits inside this device which can accept a 3.5mm signal... then buy a bluetooth transmitter/receiver combo and plug it in/tuck it inside your shirt. the receiver would be on the speaker the transmitter on the device you want to play the audio.
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something like this would likely work
http://comart.manufacturer.globalsources.com/si/6008800004502/pdtl/Bluetooth-speaker/1060662700/Micro-Box-Bluetooth-Speaker.htm
it looks rather and could probably be disassembled and some parts fit in the badge and others hidden elsewhere
or perhaps this one which looks even smaller
http://dudebrogifts.com/x-mini-tiny-bluetooth-speaker/
you might need to make your "badge" a little bigger and deeper and/or have some holes or a way for the sound to escape though.