Some scholars of Ahl al-Sunnah assert that the Caliphate of Abû Bakr al-Siddîq was confirmed by a precise statement from the Prophet (peace be upon him) that appointed him as Caliph. Other scholars hold the view that the texts only hint at his preference.
It was related that the Prophet (peace be upon him) asked a woman to come back to him for some issue. The woman asked: “What if I do not find you?”
The Prophet (peace be upon him) instructed her: “Go to Abû Bakr.” [Sahîh al-Bukhârî]
The Prophet (peace be upon him) as he neared death, asked `Aishah to call her brother and her father Abû Bakr, so he could give a written statement to Abû Bakr.
There are also hadîth regarding Abû Bakr being appointed to lead the prayers. The Prophet (peace be upon him) said: “Order Abû Bakr to lead the prayer for the people.”
None of the scholars have referred for evidence to any verse of the Qur’ân.
The above-mentioned hadîth and events, as well as many others like them, give neither direct nor indirect evidence for the appointment of Abû Bakr or anyone else as Caliph. They show the virtues of Abû Bakr and his high status in Islam.
If these narrations were evidence of the appointment of Abû Bakr as Caliph, the Companions would not have argued or disagreed, which is indeed what took place at al-Saqîfah after the death of the Prophet (peace be upon him).
These narrations do, however, indicate support for their choice of Abû Bakr as Caliph. The Companions took these incidents into account evaluating his appointment, also taking into consideration his good character and his noble attributes.
In this way, he became the first of the Rightly Guided Caliph that the Prophet (peace be upon him) commanded us to follow.
Source: Islam Today