some of the issues are certainly as above, but it should be do-able. just that you may not be confident to do it yourself, and will need a professional car audio installer to do it.
*power supply: suitably thick fused main powerwire directly from battery; routed appropriately/safely through the car into the boot; 8awg (american wire gauge) thickness should be adequate; groundwire from the amp to the chassis, securely fastened directly to bare metal
*audio signal: options: A&B: tap into the 'front' or 'rear' low level audio signals as they enter the bose amplifier; 4 wires (POS/NEG, L/R) and convert to RCA terminals, then connect to inputs on pioneer via RCA input terminal; C: tap into sub speakerwires that exit the bose amp and are therefore 'high level' (amplified) from the amp, and connect to 'high level' (speakerwire) inputs on pioneer; this signal may be too powerful even though the pioneer has adjustments
*disconnect bose subwoofer and secure new subwoofer
these are not technically difficult steps, but actually finding the right wires may be. the fact that you have to ask about it suggests to me this may fit the 'too hard basket' for yourself, but if you wish to give it a go, let us know.