'Abu' basically means father. Then I was assuming why isn't any of his sons named 'Bakr'
This is indeed a strange but acceptable kunyah or surname knowing that abu Bakr (whos real name is Abdullah ibn abi Quhafah) had three sons: Abdurrahman, Abudllah and Muhammad and three daughters: Asma'. 'Aisha and Umm Kalthoom. So it would rather sound logical if his kunyah or nickname was abu Abdarrahman or Abu Abdullah or ... or abu Umm Kalthoom.
Scholars have no clear answer for it except the fact that abu Bakr liked to be called this way. Here's a short explanation on kunyah (nickname):
The kunyah is a nickname which starts with Abu (father of) or Umm (mother of). It usually includes the name of the oldest son. It may also be just a nickname, as in the example given in the question, since Abu Bakr did not have any child whose name was Bakr. The nickname may be given because of something that is unique to that person, such as Abu Hurayrah (lit. father of the kitten). The Prophet (peace and blessings of Allaah be upon him) gave him this nickname because he would often carry a cat or kitten with him. (source islamqa #6239)
Imam an-Nawawi said in his al-Adhkaar:
"بابُ جَوازِ واستحباب اللقبِ الذي يُحبُّه صاحبُه؛ فمن ذلك أبو بكر الصديق رضي الله عنه، اسمه عبد الله بن عثمان، لقبه عتيق... ومن ذلك أبو تراب لقبٌ لعليّ بن أبي طالب رضي الله عنه، وكُنيته أبو الحسن" (source islamweb #271942)
(My own translation take it carefully:
Chapter on the permission and recommendation of a surname which is liked by his "owner":
Among this is Abu Bakr as-Sidiq may Allah be please with him, his name is Abdullah ibn 'Othman, his surname was 'ateeq ... and among this is also abu Toraab the surname of 'Ali ibn abi Talib may Allah be pleased with him and his kunyah is abu al-Hassan.
You may also read in ibn Qayyim al-Jawziyaah's tohfat al-Mawdood:
وَيجوز تكنية الرجل الَّذِي لَهُ أَوْلَاد بِغَيْر أَوْلَاده، وَلم يكن لأبي بكر ابْن اسْمه بكر، وَلَا لعمر ابْن اسْمه حَفْص، وَلَا لأبي ذَر ابْن الْمُنْذر ابْن اسْمه ذَر، وَلَا لخَالِد ابْن اسْمه سُلَيْمَان، وَكَانَ يكنى أَبَا سُلَيْمَان، وَكَذَلِكَ أَبُو سَلمَة، وَهُوَ أَكثر من أَن يُحْصى فَلَا يلْزم من جَوَاز التكنية أَن يكون لَهُ ولد وَلَا أَن يكنى باسم ذَلِك الْوَلَد (source islamweb #271942)
(My own translation take it with care)
And it is permissible to give a man who has children (sons) a kunyah which is not referring to one of his children (sons), as abu Bakr didn't have any son named Bakr, nor had 'Omar a son named Hafs, nor did abu Dharr ibn al-Mundhir have a son named Dharr , nor had Khalid a son named Sulayman, but he was called abu Sulayman, and the same was with abu Salamah, and this case applies to more than we can list (count), so the permission for having a kunyh (surname) doesn't make it necessary to have a child (son)nor to be called by the name of a child (son).
See also this fatwa on islamqa #114158 about kunyah related rulings.