You've been downvoted to hell which I don't think is a particular useful thing, but you've made an assumption that calanders have remained the same throughout history. They have not at all, and still clearly aren't today with the Gregorian, Chinese and Jewish all being used.

At this time period you are looking at the reign of Augustus the first "Emperor" of Rome. Rome had a very simple yearly naming system and that was the reign of the two consuls for that year. So for example what people refer to as 70BC would in Rome be referred to as The Year of the Consulship of Pompeius Strabo and Marcus Crassus.

Rome also occasionally used AUC, Ab Urbe Condita, meaning after foundation of the city, this date starts with the mythical founding of the city of Rome.

In Greece generally the year were dated by the games. As there four major games such as the Olympics that cycled yearly. This meant that the 174th Olympiad could be referred to in modern day as 84BC.

I hope this helps clear up that the idea if BC and AD are much more recent inventions and there wouldn't have been a panic as the calanders at the time would not have shown any sort of major event such as the turning of a millennium as happened in 2000.

I'm sorry you got downvoted, please do ask more questions to askhistorians.