A BOSE HU puts out 4 pairs of differential, line level outputs (FR, FL, RR, RL) that feed the BOSE amp. The BOSE amp then does its digital signal processing magic and spits out amplified, per speaker signals for every (usually 2 ohm) speaker (up to 9) installed in the car with dedicated wiring to each. You sorta have to make a design decision...can your sub take in L&R channels and do it's own crossover (digital or otherwise)? If not, your only option is to use the BOSE amp's internal digital x-over and couple the amplified speaker outputs (to the rear deck subs) into your new sub's inputs. Each approach needs it's own form of adaptation to avoid introducing unwanted noise into the system.
You will also need to provide high capacity power wiring to the location of your sub (and amp?). There have been several other threads I have posted to which describe how best to do this to avoid flickering lights etc. I spent a fair bit of time and energy on this thread
One other thing about BOSE systems....they typically use cheap and cheerful speaker units and then correct for their imperfect frequency response curves by pre-distorting (digitally, in software) the audio signal in the BOSE amplifier that feeds it. So re-using BOSE speakers without a BOSE amp will sound worse than just leaving things the hell alone.
so after some research, I can tap into the input on the bose amp and the output to the aftermarket amp i think, I guess the remote wire just goes into the head unit, I might add a switch to the remote wire just so i can turn off the amp when I listen to music besides rap/hip-hop, so how does the sound get to the sub?