The town of Bandon (aka Bandonbridge) Co. Cork was split between two civil parishes - Ballymodan and Kilbrogan, most of the town was in Ballymodan.
Civil registration of births started in 1864, so a baptism search is the only option for your Anne. Do you know if she had any siblings born in Ireland ?
The Church of Ireland parish for Bandon town is listed as Ballymodan or 'Ballymodan & Kilbrogan'/Bandon, and historic records for the parish are held by the RCB Library (Representative Church Body Library) in South County Dublin and cover baptisms, marriages and death/burials for the parish back to 1695. The RCBL also hold some separate records for Kilbrogan covering back to the 1750s - the National Archives of Ireland (Bishop Street, Dublin city) also hold microfilms for these parishes or at least some of the registers. .
As far as I know neither of these parishes are covered online at the moment on any of the major websites. The RCB Library is working on a project to transcribe Church of Ireland records, see the Anglican Record Project, this should eventually cover these registers, but will take some time to complete...
