I have had a look around the indexes and other resources in an attempt to help you with burial information for BRIDGET.
I thought perhaps locating the burial of other family members may guide us to BRIDGET,
(By the way, if you follow my search suggestion for the arrival in 1854, you will see BRIDGET is with the others)
This family did not use newspapers very much for family announcements and so to date I have not located a burial for her parents or siblings.
The father used EDWARD and EDMOND/MUND interchangeably and likewise the surname has either one or two R's. He appears to have been a bootmaker.
More information available if of interest
He died intestate in 1878 and administration was granted to NORAH, his widow, You can read the digitised document
http://prov.vic.gov.au/index_search?searchid=54The couple had a number of deaths of their children, both in infancy and in early adulthood.
I have not located death announcement or notice for any to this point. So nothing to point the way to BRIDGET.
Melbourne General Cemetery would be geographically likely
Sue