I would start by ordering the microfilm for the time that your family was in Bitche from your local family history library. Since you have an exact birth date for Anna, I would order tape number 1351346 that includes records from 1873-1882. Baptisms, marriages, births and deaths are all interspersed, but they are in chronological order, and normally the person's name is in the margin. Often birth records include the parents and grandparents names and where they were born, occupations, etc. Bitche is both a town name and an area name, so you may have to look at records from other nearby towns if they didn't live in the town of Bitche. You might also try Geneanet, if you haven't already.