The Boeing generic FCOM contains procedures for a PACKS OFF TAKEOFF and an APU TO PACK TAKEOFF. There is no procedure specifically for a bleeds off takeoff, although the APU TO PACK procedure states that it is "used for making a takeoff with no bleed air supplied from the engines".
The generic FCOM is not specific to a particular aircraft serial number, and there may be other procedures out there; but this is all I can find without access to your company's Boeing documents.
Would a packs off takeoff satisfy the requirements? This procedure makes no reference to an APU requirement.