Are there traditions in Shia books such as Bihar Al Anwar that suggest that the Quran is distorted? If so, how can their presence in those books be explained?
There are some hadith along those lines. It has been suggested that these are forged hadith. In some cases, when the ayah is presented differently, with insertions, it has been suggested that this may have been an explanation or gloss by the speaker which was later misunderstood as a quotation of the entire ayah.
It is true that there are a few hadith along these lines both in Sunni and Shi'i texts.