Salih narrates that Abu Huraira (may Allah be pleased with him) used to begin the prayer with "Bismillah ir-Rahman ir-Rahim."
Hadith Referenceمسند الإمام الشافعي / كتاب الصلاة / 204
Hadith Takhrijاسنادہ ضعیف جداً: فان شیخ الشافعی متروک وصالح اختلط بآخرہ لکنہ صح من غیر ہذا الطریق أخرجہ النسائی، الافتتاح، باب قراءۃ بسم اللہ الرحمن الرحیم: 906 - وصححہ ابن خزیمہ: 499 - وابن الجارود: 184 - والحاکم: 1/332۔
Anas bin Malik (may Allah be pleased with him) narrates: Muawiyah (may Allah be pleased with him) led the prayer in Madinah. In it, he recited "Bismillah ir-Rahman ir-Rahim" aloud with Surah Al-Fatihah, but did not recite "Bismillah ir-Rahman ir-Rahim" aloud with the Surah after Al-Fatihah, until he completed its recitation. And when bowing (for ruku‘), he did not say the takbir aloud until he completed the prayer. When he finished with salam, those of the Muhajirun who heard this called out from every direction: "O Muawiyah! Did you steal the prayer or did you forget?" After that, when he led the prayer, he recited "Bismillah ir-Rahman ir-Rahim" with the Surah after Al-Fatihah as well, and when he bowed for prostration, he said the takbir.
Hadith Referenceمسند الإمام الشافعي / كتاب الصلاة / 205
It is narrated from Ubaid bin Rifaa that when Muawiyah (may Allah be pleased with him) came to Madinah, he led the prayer. He neither recited the “Bismillah ar-Rahman ar-Raheem” aloud nor said the takbeer when bowing and rising. When he finished the prayer with salam, the Muhajireen and Ansar called out to him: “O Muawiyah! You have stolen the prayer. Where is ‘Bismillah ar-Rahman ar-Raheem’? And when you bowed and rose, where was the takbeer?” Later, when he led another prayer, he said: This is the matter on which they criticized me.
Hadith Referenceمسند الإمام الشافعي / كتاب الصلاة / 206
Ubaid bin Rifaa narrates from Muawiyah (may Allah be pleased with him), from the Muhajireen and Ansar, a narration similar to (the previous hadith) or with the same meaning, which does not contradict the (previous one). Imam Shafi’i (may Allah have mercy on him) says: In my view, this chain of narration is more reliable than the first chain.
Hadith Referenceمسند الإمام الشافعي / كتاب الصلاة / 207
Nafi' narrates that Ibn Umar (may Allah be pleased with them both) would not leave out "Bismillah ir-Rahman ir-Raheem" along with Surah Al-Fatihah and the following Surah.
Hadith Referenceمسند الإمام الشافعي / كتاب الصلاة / 208
It is narrated from Anas (may Allah be pleased with him) who states that the Prophet (peace be upon him), Abu Bakr, Umar, and Uthman (may Allah be pleased with them) used to begin the recitation with "Alhamdu lillahi Rabbil 'alamin."
Hadith Referenceمسند الإمام الشافعي / كتاب الصلاة / 209
Hadith Takhrijأخرجہ مسلم، الصلاۃ، باب حجۃ من قال لا یجہر بالبسملۃ: 399۔