BULK INSERT continue on PRIMARY KEY error
I think a good approch would be to have a staging table (without PK constraint).
You will load your data from your bulk command into this table and then, you should be able to script down the logic you want to implement into a store procedure that you can run after
Ex: Check for duplicate, log them to another table or send a mail, delete the duplicate base on some logic and then insert the remaining rows into the target table.