You don't make it clear if you want to send audio TO the boombox or FROM the Boombox.
If it has an aux input you can connect a bluetooth receiver to it and send audio to it for playback.You can't use an input as an output so you can't send audio out from that. If the boombox has a headphone output then you can use that to connect a bluetooth transmitter to send audio to BT clients like speakers or headphones.