When resuming the reading of the Qur’aan, do one have to say bismillah or is this an innovation?
The answer is that as long as you are reading a Surah from the beginning you say Bismillah except Surah At Tawbah as there is no Bismillah in its beginning. As for reading a part of a Surah or an Ayah, then there is no Bismillah and it is considered as inventing something which is not there. Rather, one can say: آعُوْذُ بِاللَّهِ مِنَ” الشَّيْطَانِ الرَّجِيمِ”
or “اَللَّهُمَ إِنِّي أَعُوذُ بِكَ مِنَ الشَّيْطَانِ الرَّجِيمِ مِنْ هَمْزِهِ وَنَفْخِهِ وَنَفْثِهِ” without Bismillah. The reference of validity of these wordings posted above is here, here, and here.
And Allah Knows best.
[Paraphrased from one of Faisal Ibn Abdul Qaadir Ibn Hassan’s classes]