The info in your question is very vague.You will have to have more detail to get helpful responses.
I think it is important for you as a start to learn a bit about the history of the region and you can do that at http://www.bukovinasociety.org/http://www.bukovinasociety.org/
Bukovina prior to WW I was part of the Austro-Hungarian Empire.The surname certainly sounds Germanic so the reference to "British Subject" might be a red herring unless it occurred later in her life.
If the family indeed moved from Bukovina to Russia, you will need a place name or at least a region to move along with your research.There were Germans scattered all through the Black Sea region in Russia to the east of Bukovina.They could have gone there or even further afield.Knowing her faith origin may also help a little - Catholic, Lutheran, Jewish??
Where did they settle after leaving the old country - Canada, US, Australia, Brazil?They often migrated with others to a community where friends or relatives had already gone.Have you found a passenger ship list that might state a place of birth?
If you can provide more detail, we may be able to help more.