Can a Bishop forbid some literature to the faithful under his rule? Can a Bishop, forbid the reading of some books (or any kind of literature) to faithful under his rule, in such a way, that it would be sinful for the faithful to not follow his advice?
Yes, as canonist Dom Augustine writes on 1917 can. 1384 (cf. 1983 CIC 823-24),


  § 1. The Church has the right of requiring that books that have not been recognized by her prior judgment not be published by the faithful,1 and that those published by anyone be prohibited for a just cause.2


1. "preventive censorship (praevia librorum censura)," for Catholics only2. "vindicates to the Church the right of prohibiting any and all books which she considers objectionable," even for non-Catholics,

natural law grants "the right to control the reading of her children" to


  Paternal as well as political authorities [who] have the natural right to ward off anything that may endanger the moral and physical welfare of their subjects, and to protect them against bad surroundings, company, literature, etc., in fact anything that is apt to cause insubordination, anarchy, or moral decay. The Church, being an autonomous society, with subjects for whom she is responsible within her own sphere cannot be destitute of the authority and power which enables her to keep her children uncontaminated and to safeguard them against the danger of perversion. Of all the dangers that imperil man's salvation bad literature is perhaps the most destructive. Hence the right to control the reading of her children cannot be denied the Church even from the purely natural point of vantage. Historical facts amply confirm the necessity of preventive censorship in Church and State.11. Cfr. the classical work of J. Hilgers, S. J., Der Index der verbotenen Bücher, 1904.