Police said forensic tests have confirmed the remains belonged to a woman aged 35 or more.
They do not yet know the identity of the person and said further tests would be carried out to establish that.
The bone fragments were found on the edge of the loch near Tarbet in Argyll and Bute on August 3.
Ms Pilley, a 38-year-old bookkeeper from the Stenhouse area of Edinburgh, vanished on her way to work in the city centre in May 2010.
Last year a major search of the Argyll Forest was carried out but her body was never found.
It is understood the bones are not linked to the high-profile cases of of Ms Pilley, missing woman Lynda Spence or Margaret Gardiner, whose body has never been found.