Imam al-Sha'bi (may Allah have mercy on him) says: When Sayyidah Fatimah (may Allah be pleased with her) fell ill, Sayyiduna Abu Bakr (may Allah be pleased with him) came to her. He asked permission, and Sayyiduna Ali (may Allah be pleased with him) said: "O Fatimah! Abu Bakr has come; he is asking permission to come in to you." Sayyidah Fatimah (may Allah be pleased with her) said: "Would you like me to give him permission?" Sayyiduna Ali (may Allah be pleased with him) said: "Yes." So Sayyidah Fatimah (may Allah be pleased with her) gave permission. He came in to Sayyidah Fatimah (may Allah be pleased with her), sought to please her, and said: "I did not leave my home, wealth, family and clan except for the pleasure of Allah, the pleasure of the Messenger of Allah (peace and blessings be upon him) and the pleasure of you, the People of the House." Then he sought to please her until she was pleased.
This is a mursal (a report whose chain omits the Companion) that is hasan (good), with an authentic chain.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب قسم الفيء والغنيمة / 12735