The Bible regularly refers to a calendar. It mentions months by number, and sometimes by name. It gives the dates in the relevant months on which the feasts, which God prescribed, had to be held. And then, of course, the unbroken pattern of six days’ work and the seventh day rest underlies all the reckoning of time, just as does the cycle of night and day and the seasons of the year. Even at the time of the deluge, exact dates were given for when the rain began and for when Noah disembarked a year later. And we see that even Noah counted the days in sevens. 
What sort of calendar was it?
It was not our Roman calendar. That came much later. It was also not the current Jewish calendar. That was introduced by the Pharisees about the middle of the first century of the Christian era. The Dead Sea Scrolls (DSS) shed a lot of light on this matter. And they reveal the bitter contention over the Pharisaic meddling with the Bible calendar. The original Bible calendar, which I call the “Sacred Calendar”, obviously was different.