According to the first point in this document (accessed 8 March 2018 from the Irish Department of Foreign Affairs website: https://www.dfa.ie/) it would seem that you will be able to travel to the Republic of Ireland with a BIVS-endrosed valid short-stay visa:
"The British-Irish Visa Scheme allows for mutual recognition of short-stay visas between the UK and Ireland. This means that a British short stay visa will be valid for travel onward to Ireland, and an Irish short-stay visa will be valid for travel onward to the UK. Visas that are valid for use under this scheme will have ‘BIVS’ endorsed on them."
As for traveling to Northern Ireland, there should be no issue whatsoever, as Northern Ireland is part of the UK.
However, it may be the case that your friend cannot travel to Ireland, depending on her visa. This is based on my personal knowledge of 2 people (1 Japanese and 1 Chinese) who lived and worked in Ireland under long-term visas, but could not travel to the UK without obtaining a UK visa.
This suggests that the BIVS does not apply to long-term or working visas.