As of now, we don't know anything about the Bioshock movie, which Netflix is filming. In an interview,  the producer of the movie, Roy Lee, only said the Bioshock Movie will be based on the first game of the series, which was released in 2007. 
Work on the script is still being done and has not been completed. The director of the movie is Francis Lawrence, who is also working on  The Hunger Games: Sunrise.