Is the Bill Of Sale required for deregistration?
In the US you don't need a bill of sale because the aircraft may not have been sold. The FAA's definition says:


  Deregistered Aircraft An aircraft that has been removed from the U.S. Civil Aircraft Register at the owner's request. Aircraft are
  generally removed for the following reasons: exported, destroyed,
  salvaged, dismantled, or permanently retired from service.


There would be no bill of sale for a destroyed aircraft, for example.

If you're asking about handling the FAA registration when you sell an aircraft, according to AOPA's guide you have to sign and return the current registration certificate, and the FAA will issue a new one to the buyer.