When and how many times should we recite Bismillah in salah?
Bismillah is not said in Salah anywhere except before the recitation of the Quran during qiyam.
And on this there is disagreement. Because of the dispute on whether Bismillah is a proper verse of Surah al-Fatihah and the other surahs. Some have held that it is not part of any Surah (except 27:30). Some have held that it is also a proper first verse of Surah al-Fatihah but not any other surah. And some have held that it is a proper first verse of every Surah except Surah at-Tawbah.
In short, the Hanafis and Hanbalis consider saying it to be recommended not obligatory. The Hanafis limit this to the one before al-Fatiha and do not consider it recommended to recite it before the second surah. The Shafi'is consider it obligatory, and this is also one view among the Hanafis. And the Malikis hold that it should not be recited and consider it makruh, although there are also some variants on this in the madhab.
For further details you can see:
Mawsoo‘ah al-Fiqhiyyah (Arabic) or
Islamic Jurisprudence According To The Four Sunni Schools [page 333-334] (English)
Bismillah is recited at the beginning of Surah Al-Fatihah, which is a mandatory component of the prayer. However, there is no specific requirement to recite Bismillah before any other Surah in the prayer.
According to the majority of Islamic scholars, it is recommended to recite Bismillah silently before beginning to recite Surah Al-Fatihah in every Rak'ah (cycle) of the prayer. This means that Bismillah is recited once in each Rak'ah, at the beginning of Surah Al-Fatihah.
However, there is some difference of opinion among Islamic scholars on this issue. Some scholars believe that Bismillah should not be recited aloud in the prayer, while others believe that it should be recited both aloud and silently. Nonetheless, the majority of Islamic scholars agree that reciting Bismillah silently before Surah Al-Fatihah in every Rak'ah of the prayer is recommended (mustahabb).