It is narrated from Hazrat Anas (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) and the three Caliphs (may Allah be pleased with them) used to begin the recitation in prayer with "Alhamdulillahi Rabbil 'Alamin" and they did not mention Bismillah at the beginning or end of the recitation.
Hadith Referenceمسند احمد / مسند المكثرين من الصحابة / 13337