I think you might find it's Radcliffe which is close to Bury Lancashire and may have come under Bury unless there is a Ratcliffe I haven't looked. Closest I can find is
Name: Elizabeth Harrison
Baptism Date: 18 Sep 1859
Parish: Heywood, St James
Parish as it Appears: Bury, St James
Father's Name: Joseph Harrison
Mother's Name: Mary Ann Harrison
Reference Number: GB127.L170/1/1/2

Regards