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In order to understand what led Abu Bakr (r.a) to defeat the Byzantium Empire you would have to first go to the Quran.

The following verses of the Quran can begin answering this question for us:

Surah Taubah Verses 107

AND [there are hypocrites] who have established a [separate] house of worship in order to create mischief, and to promote apostasy and disunity among the believers, and to provide an outpost for all who from the outset have been warring against God and His Apostle. And they will surely swear [to you, O believers], "We had but the best of intentions!" - the while God [Himself] bears witness that they are lying

These were revealed as a warning against a man named Abu Amir who was a Christian, fled to Byzantium Empire and kept instigating the emperor Heraclius to conquer Arabia and destroy Madinah, which was the capital of the Muslims. He had left behind his secret followers i.e. Hypocrites (who pretended to be Muslims) and ordered them to build a mosque so that Muslims could be divided and if he succeeded in doing that then the military support of the Muslims will be diminished which will make it easy for them to be destroyed if the Byzantium Army invaded Arabian Peninsula. Once Allah (swt) revealed the knowledge of this plot to Prophet Muhammad (SallAllahu alaihi Wassallam) he had that mosque demolished and as a result of this plot led an army to face the Byzantiums in an expedition which called Tabuk.  

The above Verses are part of the Surah Taubah, chapter 9, which deals mainly with the expedition of the Tabuk. This man named Abu Amir was a Christian monk who had followers in Syria as well.

The spread of Islam throughout the Arabian Peninsula which bordered the Byzantium empire was also perceived as a threat to them, therefore when the news reached Madinah that the empire was gathering forces to march on the peninsula, the Muslims led this expedition. However this expedition came to an end soon after the news came that either the Byzantium forces are not ready to invade or they had given up the idea. Since Islam supports Jihad in self-defense only the Muslims abandoned the idea to fight the Byzantiums.

In those days 2 powers fought each other in the Middle East to control power, the Persians and the Byzantium. They never looked at the desert Arabs and never wanted to even go to the deserted dry land. But by the time Abu Bakr (r.a) became the Muslim Caliph and the Muslims gained strength, they were looked upon as inevitable threat by these 2 super powers that needed to be conquered and finished immediately. Basically if the Muslims had not acted in self defense against these powers that bordered them, they would have been eliminated instead.