You would need to have a subwoofer with a built in crossover to extract low frequencies for the subwoofer and push out the mids and highs to speakers such as your bose. Replacing your sub with another like the one you have would solve nothing.
You could also try to find a sound card that has an actual subwoofer output via 3.5mm
My Soundcard has an output for center/subwoofer. I'm assuming you meant an exclusive output for just subwoofer?
Either way it appears you answered my question. I appreciate it thank you.