Pearls from Bahrain are always going to be older pearls. They will also be solid nacre.
The most notable thing about these pearls is that they are usually a bit yellowish. You would not be able to see a nucleus either, as the pearls have no nucleus. The pearls can easily be mistaken for freshwater pearls, which would then have not very much value. I would suggest sending the pearls to a gemological lab to verify the origin. If you are here in Europe I would suggest the EGL. I think the best in the USA is the GIA. You may want to check locally to see if there are any pearl experts with experience in dealing with Bahrainian pearls. But you need for sure a pearl expert not a jeweler to tell you this because they will certainly claim as freshwater pearls.