(a) Sayyiduna Anas (may Allah be pleased with him) says that the Prophet (peace and blessings be upon him) prayed behind Sayyiduna Abu Bakr (may Allah be pleased with him).
(b) Imam al-Shafi'i (may Allah have mercy on him) says: If the Prophet (peace and blessings be upon him) prayed behind Sayyiduna Abu Bakr (may Allah be pleased with him) on one occasion, nothing prevents that on another occasion Sayyiduna Abu Bakr (may Allah be pleased with him) prayed behind him (peace and blessings be upon him).
Note: Musa bin Uqbah mentions in his Maghazi that Sayyiduna Abu Bakr (may Allah be pleased with him) led one rak'ah of the Fajr prayer on Monday, the very day on which the Prophet (peace and blessings be upon him) passed away. The Prophet (peace and blessings be upon him) felt some recovery, so he (peace and blessings be upon him) came and prayed one rak'ah with Sayyiduna Abu Bakr (may Allah be pleased with him). When Sayyiduna Abu Bakr (may Allah be pleased with him) gave the salam, he (peace and blessings be upon him) stood up and completed the second rak'ah. It is possible that this is the prayer meant by the one who reported that the Prophet (peace and blessings be upon him) prayed behind Sayyiduna Abu Bakr (may Allah be pleased with him) during his illness, and that the prayer which Sayyiduna Abu Bakr (may Allah be pleased with him) prayed behind him during the days of his illness was the Zuhr prayer, which took place on Sunday or Saturday, as is also reported from Sayyidah Aishah (may Allah be pleased with her) and Ibn Abbas (may Allah be pleased with them both). So there is no contradiction between them, and it is valid to use the first report as evidence.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 5087