The Gregorian calendar has a leap year cycle of 400 years = 146097 days. Since this happens to be a whole number (20871) of weeks, any date will always be on the same day of the week as its 400th anniversary. Also note that nn BCE = -(nn-1) CE = 1-nn CE, with the "1" being an adjustment for the non-existence of a year zero between 1 BCE and 1 CE.
Putting this together, a calendar for the year n BCE will be identical to the calendar for the year 400m+1-n, where m is any integer.
For example, the calendar for 44 BCE is equivalent to that of 1957 CE, a common year starting on Tuesday, March 15 on a Friday.
Of course, this is for the proleptic Gregorian calendar, not the actual calendar in use at the time. For historical dates, you need to be aware of:
- When the given location transitioned from the Julian calendar to the Gregorian calendar.
- The leap year error affecting dates between 44 BCE and 12 CE.
- The haphazard nature of the Roman calendar before Julius Caesar's reform.
- The fact that the seven-day week wasn't used (except in Jewish communities) until Christianity became popular.
Also, the date of Easter (and Easter-relative holidays like Mardi Gras) includes a lunar calculation and doesn't repeat every 400 years as the days of the week do. But there'd be no reason for anyone to observe that holiday prior to the crucifixion of Jesus of Nazareth (circa 33 CE), so that's probably not a problem.