I would use a French triple milled soap with Shea Butter, the different versions of Aleppo soap and other mediterranean soaps such as the original Savon de Marseille are good body bars and Aleppo soap makes a good shampoo but they do not have the added moisturisers that modern products contain. However if you just want a normal soap they are all good!
I have picked up loose hand made Turkish soaps in Turkish grocery stores, but I haven't heard of Bittim soap before. Is all Bittim soap made of Wild Pistachio oil and Terebinth Tree oil?