Abu Bakr (ra) was sent to Banu Kilab tribe, the reports on this expedition, don’t tell us a lot, other than the Muslims had a battle. It does not give us any more details. Sunan Abi Dawud:
AbdurRahman ibn Tarafah said that his grandfather Arfajah ibn As’ad who had his nose cut off at the battle of al-Kilab got a silver nose, but it developed a stench, so the Prophet ordered him to get a gold nose. (Sunan Abi Dawud Book 35, Hadith 4220)
Dr. Shawqi Abu Khalil:
“The expedition of Abu Bakr As-Siddiq to Najd in Sha’ban 7 AH. He went to Najd where there were groups of Banu Kilab.” 
I would most probably say that Abu Bakr (ra) was sent as a result of the killing Muslims, previous to this incident. Not long before this expedition, it is reported by Islamic scholar Allama Shibli, that a number of missionaries who preached the Message of Islam were slaughtered by some men among the Banu Kilab tribe:
“SIRYA BI’R MA’UNA
In the month of Safar of the same year, Abu Bara, the chief of the tribe of Kilab came to the Prophet (p) and asked him to send with him a few Muslims in order to preach to his tribe. The Holy Prophet (p) remarked that he feared mischief from Nejd. Abu Bara replied that he himself stood their security. The Prophet agreed and sent 70 Ansaris with him. These were all very pious men of saintly habits, the majority belonging to the companions of the Suffa. Their daily routine had been to collect fuel from the forest, which they sold in the evening and shared the proceeds with the other members of the Suffa.
These men made a halt at a place known as Bi’r Ma’una. Through Haram Ibn Milhan, they sent the Prophet’s letter to Amir Ibn Tufail, the chief of the tribe. Amir killed Haram Ibn Milhan. He also hurried up his men to the neighbouring tribes of Usiyya, Ra’l and Dhakawan, asking them to come prepared.
Thus a big force was collected, which advanced forward under the command of Amir. The companions were waiting for the return of Haram Ibn Milhan; and when he did not turn up they themselves moved forward. In the way they came face to face with Amir. The infidels surrounded the Muslims on all sides and killed all of them, except Amr Ibn Umayya whom Amir spared saying that his mother had taken a vow to free a slave and so he was setting him free. Then he cut his locks of hair and left him. The Prophet had never been so grieved as when this mishap was reported to him. For a whole month the Prophet (p) prayed against these evil-doers after his morning prayers.
Amr Ibn Umayya, on his way back, killed two men from the tribe of Amir, whom the Prophet (p) had given immunity.
Amr did not know of it. He thought he was getting revenge on Banu Amir for their faithless conduct towards the Prophet’s companions. The Prophet (p) expressed his displeasure when it was made known to him, and announced the payment of their blood-money to be made.” 
Given the fact that the report do not give us specific information as to why this expedition took place, we can safely say that this expedition by Abu Bakr Siddiq was most probably sent to deal with those treacherous members of banu Kilab, who had killed Muslims.
Before Abu Bakr’s expedition to Banu Kilab, they have attacked and killed Muslims:
1. The Expedition Of Dahhak al-Kilabi
2. Expedition Of Muhammad Ibn Maslamah To Banu Bakr
Don’t forget to follow Discover The Truth on Facebook and Twitter. PLEASE help spread the word by sharing our articles on your favourite social networks. Thank You!
 Al-sirah Al-Nabawīyah: Atlas On the Prophet’s Biography, Places, Nations, Landmarks, by Dr. Shawqi Abu Khalil page 205
 Sirat -un- Nabi [Sallallahu Alaihi Wasallam] By Shaykh Allamah Shibli Nomani (r.a) – Volume 2, page 77 – 79