Weeks? Months?
I assume you could travel by sea, but I really don't know, that's why I'm asking.
Check out ORBIS: The Stanford Geospatial Network Model of the Roman World, which "reconstructs the time cost and financial expense associated with a wide range of different types of travel in antiquity." You tell it your destination and point of departure, what time of year you're traveling, and other info. Very detailed. It says it reflects the conditions of ~200 CE, so later than what you're looking for, but still maybe a good starting point. Maybe someone with more knowledge of Rome could weigh in on its accuracy.