A guide bushing for a coring reamer having a tapered member with its largest diameter at its first end so that the guide bushing frictionally engages an internal surface of the reamer with a line contact. The guide bushing has a passage sized to slidably receive a guide pin. In use, the bushing advances in the proximal direction within the coring reamer along a guide pin while the excavated bone enters the passageway through the reamer. A storage package specifically designed for the reamer assembly is employed to remove the excavated bone from within the reamer. The package has a closed distal end and an open proximal end closeable with a cap. With the coring reamer received in cantilevered fashion through a central opening of the cap of the tube, and with an adapter that couples the coring reamer to a handpiece installed, a wrench is placed over the adapter and turned while the user grips peripheral surfaces of the cap to prevent rotation of the coring reamer. A plunger is inserted through the opening through the coring reamer from the proximal end and is pushed through the reamer until the bone core and bushing fall out of the distal end of the coring reamer.