Ayesha reported,
She said, "Abu Bakr came riding on his horse from his dwelling at Sunh, dismounted, and entered the mosque. He did not speak to the people but went straight in to see Ayesha. He went to the Prophet ﷺ, who was covered with a striped Yemeni cloak. He uncovered his face, leaned over him, kissed him, and wept."Then he said, "May my father be sacrificed for you, Prophet of Allah. Allah will not combine two deaths upon you. As for the death decreed for you, you have already died it."Abu Salama said, Ibn Abbas informed me that Abu Bakr 
went out while Umar was addressing the people. Abu Bakr said to him, "Sit down."Umar refused.He said again, "Sit down."Umar refused.So Abu Bakr proclaimed the testimony of faith, and the people turned to him and left Umar. Abu Bakr said, "To proceed. Whoever among you used to worship Muhammad ﷺ, indeed Muhammad ﷺ has died. And whoever used to worship Allah, indeed Allah is Living and does not die. Allah the Exalted said, 'Muhammad is no more than a messenger,' up to His words, 'the grateful'" [Aal Imran 3:144].By Allah, it was as if the people did not know that Allah had revealed this verse until Abu Bakr recited it. The people then took it from him, and not a single person was heard except reciting it.In another narration she said, "Then Abu Bakr came. The veil was lifted, and he looked at him and said, 'We belong to Allah, and to Him we return. The Messenger of Allah ﷺ has died.' Then he approached him from the direction of his head, lowered his face, and kissed his forehead. Then he said, 'O Prophet!' He raised his head, then lowered his face again, kissed his forehead, and said, 'O chosen one!' Then he raised his head, lowered his face, kissed him, and said, 'O dear friend! The Messenger of Allah ﷺ has died…'" The hadith continues at length and will appear in its place.
Azami 3598
Sahihعن عائشة زوج النبي ﷺ
قالت: أقبل أبو بكر على فرسه من مسكنه بالسنح حتى نزل، فدخل المسجد فلم يكلم الناس، حتى دخل على عائشة، فتيمم النبي ﷺ وهو مسجى ببرد حبرة، فكشف عن وجهه، ثم أكب عليه فقبله، ثم بكى فقال: بأبي أنت يا نبي الله، لا يجمع الله عليك موتتين، أما الموتة التي كتبت عليك فقد متها. قال أبو سلمة: فأخبرني ابن عباس: أن أبا بكر رضي الله عنه خرج وعمر رضي الله عنه يكلم الناس، فقال: اجلس، فأبى، فقال: اجلس، فأبى، فتشهد أبو بكر، فمال إليه الناس وتركوا عمر، فقال: أما بعد: فمن كان منكم يعبد محمدا ﷺ فإن محمدا ﷺ قد مات، ومن كان يعبد الله فإن الله حي لا يموت، قال الله تعالى: {وما محمد إلا رسول} إلى قوله: {الشاكرين}. والله، لكأن الناس لم يكونوا يعلمون أن الله أنزلها حتى تلاها أبو بكر، فتلقاها منه الناس، فما يسمع بشر إلا يتلوها. وفي رواية قالت: ثم جاء أبو بكر، فرفعت الحجاب، فنظر إليه، فقال: إنا لله وإنا إليه راجعون، مات رسول الله ﷺ ثم أتاه من قبل رأسه فحدر فاه، وقبل جبهته، ثم قال: وا نبياه، ثم رفع رأسه، ثم حدر فاه، وقبل جبهته، ثم قال: وا صفياه، ثم رفع رأسه، وحدر فاه، وقبل، وقال: وا خليلاه، مات رسول الله ﷺ… الحديث بطوله وسيأتي موضعه.
Bukhari narrated it in the chapter on funerals (1241, 1242) from Bishr bin Muhammad, who said, Abdullah informed us, saying, Mamar and Yunus informed me, from Zuhri, Abu Salama informed me from Ayesha, and he mentioned it. Bukhari also narrated it in the chapter on military expeditions (4455) through another route from Ayesha and Ibn Abbas, that Abu Bakr kissed the Prophet ﷺ, in a shortened form, making the hadith part of the narrations of both Ayesha and Ibn Abbas together.The second narration was related by Imam Ahmad (25841) from Bahz, who said, Hammad bin Salama narrated to us, saying, Abu Imran Jawni informed me, from Yazid bin Babnus, who said, I and a companion of mine went to Ayesha and sought permission to see her. She threw out a cushion for us and drew the curtain toward herself, and he mentioned the hadith in a lengthy account which will come in its proper place. Its chain of transmission is hasan on account of Yazid bin Babnus, for Daraqutni said of him, "There is no harm in him," and Ibn Adi said, "His hadiths are well known," and Ibn Hibban mentioned him among the trustworthy narrators. A narrator like this has his hadith graded hasan. What has been reported from Abu Hatim, that he said of him, "unknown," has not been established.As for Abu Bakr's statement, "Allah will not combine two deaths upon you. As for the death that was decreed for you, you have already died it," perhaps he intended by this to respond to those who thought that he ﷺ had not died but had merely concealed himself from people's sight, so he informed them that he had died the real death just as any human dies, in accordance with the words of Allah Most High, "Every soul will taste death" [Al Imran 3:185]. Ibn Hajar has mentioned other explanations besides this one.As for what was reported from Ayesha, who said, the Prophet ﷺ kissed Uthman bin Mazun while he was dead, and it is as if I can still see his tears upon his cheeks, this is daif. It was narrated by Abu Dawud (3163), Tirmidhi (989), and Ibn Majah (1456), all through the route of Sufyan, from Asim bin Ubaydullah, from Qasim bin Muhammad, from Ayesha, and he mentioned it. The hadith is also in the Musnad of Imam Ahmad (24165) through this same route. Tirmidhi said, "hasan sahih." Hakim also reported it (1/361) through this route, except that he did not pass judgment on it but rather said, "This is a hadith circulated among the scholars, except that the two Shaykhs [Bukhari and Muslim] did not rely on Asim bin Ubaydullah as evidence, and its authentic corroborating witness is the well-known hadith of Abdullah bin Abbas, Jabir bin Abdullah, and Ayesha, that Abu Bakr Siddiq kissed the Prophet ﷺ while he was dead." End of quote.I say, it is as he said, for they have unanimously agreed on weakening Asim bin Ubaydullah bin Asim bin Umar bin Khattab Madani. Ibn Main said, "daif," and Abu Hatim and Bukhari said, "His hadith is objectionable." I think this hadith is among his objectionable narrations, for the established and sound account is that Abu Bakr Siddiq kissed the Prophet ﷺ while he was dead.Among his objectionable narrations and errors is also what he related a second time, from Ubaydullah bin Abdullah bin Amir bin Rabia, from his father, who said, I saw the Prophet ﷺ kiss Uthman bin Mazun. This was narrated by Bazzar in Kashf Astar (809), and Haythami said in Al-Majmu (3/20) that its chain of transmission is hasan. I say, rather it is daif on account of this same Asim bin Ubaydullah.