The coffin was taken in to Brahms's Herzlich Tut Mich Verlangen.
The first hymn sung was The Lord's My Shepherd I'll Not Want.
Bible readings were given by Pc Bone's colleagues Inspector Jane Brown and Pc Tracey Miskell.
GMP chaplain Charles Nevin read the poem She Is Gone, while mezzo-soprano Iona Fisher gave a performance of Beyonce's version of Ave Maria.
Police and the public gathered at the rear of the cathedral to listen to the service broadcast on loudspeakers.
Fallen police hero Fiona Bone was kind and gentle but also a "brave rock of a woman", mourners at her funeral in Manchester have heard.
Police officers and the public turned out in force again today for the funeral of a second policewoman killed in a gun and grenade attack.
The funeral of Pc Fiona Bone, who was gunned down in Hattersley last month, will be held at Manchester Cathedral.