Bohdiewicz is a really difficult name to pin down because over the years Jews have been persecuted in many countries and have been deported such as those from Czechoslovakia who went to Poland in WW2 or the Armenians who got out in 1915.
As a consequence they are now spread over many nations.
It would be useful to know where and when they arrived in their new country so that the probable historic event could be identified to give a probable origin country for your particular family. Perhaps you have this information and are are able to understand the motivations for their movements.
My own gut feeling with this name is Czechoslovakia but there are too many possibilities to be certain.