as salam alaikum
reading the Bible in itself is not a problem. The Muslim person should be aware that the books included in the modern-day Bible are translations of non-original sources and therefore its accuracy cannot be confirmed. The original books have been tampered while the modern versions contain both correct and incorrect information; it is therefore difficult to discern truth from falsehood for common people.
Bible can be compared to books of hadith with no chain of transmission. It is possible to compare its content with the Qur'an, mutawatir narrations and well-established traditions, and also to study it in the light of historical facts. Today it cannot be considered an heavenly book according to Islamic perspective.
With prayers for your success.