If you asked someone living in the Roman Empire circa 100 CE what year they were living in, what would they say?

It depends on which part of the Roman Empire they were in. Consular years were important at Rome during the Republic, and Imperial regnal years were increasingly important during the Empire, but the different regions of the Roman Empire had year systems that predated their incorporation into the Empire, such as Olympiads, the Seleucid era, the founding of their local kingdom or city, and so on. Some areas also started year systems after being incorporated into the Empire, such as the Spanish Era and the Indiction. Dating from the founding of Rome (AUC) wasn't commonly used.

Which dating system was used would have depended on context and meaning. Keeping track of the history of your local city council? You'd continue to use the year system that had always been used for that purpose. Keeping track of taxation? You'd use the Indiction, if that's how your tax cycle was set by the authorities. Keeping track of Imperial business? You'd use the consular year or the regnal year, whichever was more meaningful to you. Trying to write a chronicle and integrate multiple year systems together? Things would get messy, especially when trying to align regnal years with other dating systems, as the last year of the old ruler is also the first year of the new ruler.

This accumulation of different dating systems was partially addressed in the fourth century CE by the universal chronicle of Eusebius, which included a concordance of chronologies in tabulated form, with each column ending with conquest by the Roman Empire until there was only one column left, namely the one for the Roman Empire. Later chroniclers continued that "single line" - but that didn't mean there was agreement on a single dating system to use in their chronicles.

For example, Hydatius of Lemica, a Spanish chronicler from the fifth century CE, refers in his Chronicle to

Imperial regnal years
Olympiads
Consular years (three times)
the Indiction year (once)
AUC (once)

Later copyists inserted references to the Spanish Era and the Year of Abraham to their copies of Hydatius' Chronicle.

Hydatius tried to keep the 4-year Olympiads aligned with regnal years in his Chronicle - he included an explanation of how there weren't 5 years in each Olympiad the first time it came up (chapter 26, where he explains how the last year of Theodosius' reign was also the first year of the reigns of Arcadius and Honorius). This was probably a greater problem for historians than in day-to-day life.

Some references (sorry they're all old, I'm referring back to research I did in the 1990s, there's probably more up-to-date resources out there):

Breisach, E. Historiography: Ancient, Medieval and Modern. Chicago, 1983.

Muhlberger, S. The Fifth-Century Chroniclers: Prosper, Hydatius and the Gallic

Chronicler of 452. Leeds, 1990.

Neugebauer, O. "On the 'Spanish Era'." Chiron, 11 (1981), pp.371-380.