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.
As the funeral cortege arrived at the cathedral spontaneous applause rang out and a lone Scottish bagpiper played a mournful lament.
A large portrait photo of Pc Bone was carried into the cathedral, followed by her coffin, draped in black cloth and carried by six of her police colleagues.