In my opinion, bread and circuses was more of a symptom than a cause.
In the 2nd and 1st centuries BC, as the Romans were expanding out from Italy into North Africa, Spain, Greece, and what is now Turkey, the people of influence (generals and politicians) were accumulating vast amounts of wealth, in the form of loot, land, and slaves. They used their newly-obtained wealth to buy up lots more land and establish huge agricultural operations, both in Italy and abroad.
At the same time, the small farmers that had formed the backbone of the economy and military, were in big trouble. They couldn't compete with the large farming establishments, which had the advantage of mass production, and were run off of the cheap labor of all the newly-arrived slaves. These small farmers had to sell their land to the wealthy people. They simply couldn't continue to make a living as farmers. These dispossessed people moved into the cities, where they formed a large group of poor and desperate people.
So we had a huge wealth gap forming, where the top 5% had something like 80% of the wealth. This is far worse than the wealth gap we see today, and there were lots of problems.
This new class of urban poor was typically too poor to even afford enough food to survive and employment was often difficult to find. As a result, they tended to get pretty cranky and riot a lot. So in order to keep this under control, the poor Roman populace got bread and circuses.
A populace that was getting free food and entertainment was a lot less likely to cause problems and revolt, so the wealthy people in society spent large amounts of money on free grain and free entertainment.
It was part of the culture of Rome for the wealthy to give stuff away to show how awesome they were. As they got wealthier, it wasn't a problem to give away lots of stuff. This was known as the patron-client system. In return for free stuff and favors, the recipients were expected to support the person giving them stuff by voting for them (or their allies) and attacking opponents.
The politicians shamelessly used their vast wealth to buy loyalty and used angry mobs under their control as political tools. It went downhill quickly from there as the Roman Republic slid into power grabs, civil war, and the eventual establishment of the Imperial system.
The emperors solved the political instability, but the wealth gap became even worse. At some points, the emperor personally controlled something like 80% of the wealth of the empire, with most of the remaining 20% being controlled by wealthy families.
The majority of the populace was poor, completely apathetic when it came to politics, and they had very little hope of improving their lot in life. This is considered to be one of the many reasons for the weakening of the Roman Empire. The weakening and eventual downfall as a complex thing that stemmed from a variety of factors working together, and this is just one of them.
If anyone is interested, I very much recommend the (now completed) podcast: The History of Rome. Mike Duncan makes Roman history both interesting and entertaining.