I hesitate to go down the road of telling you how to hook your BFD to a speaker since it is fraught with problems - the least of which is shorting out your speaker amplifier.
But either way, it's not that difficult.
There are a couple pieces of information that we need to know.
1. Is the Negative (-) terminal on the subwoofer speaker wire at ground potential?
This is essential since some amplifiers rely on a bridging technique to boost the power. I don't have a schematic of your speaker system with amplifier, so I can't determine this without you measuring it.
With the power off you need to measure with a multimeter on the lowest scale between the Negative (-) subwoofer speaker wire terminal (at the speaker) and ground of the amplifier. Be sure there is a short indicated.
2. What is the rated power (watts) of the subwoofer amplifier? This is necessary to roughly calculate the attenuation required to bring the signal to a line level that the BFD is familiar with.
3. What is the impedance of the subwoofer driver in ohms. (i.e. 8 ohms or 4 ohms)
3. Can you solder? If not, better forget it.
brucek