I've just got back from the Pitt Rivers Museum and there is a fascinating collection of fire making tools there, spanning 2000 BC to the early 1900s. Much of the collection dates from the late 1800s to the early 1900s but there is a wooden hearth, with a drilled impression in it that dates from 2000 BC.
Aside from that there are hand drills, thong drills, bow drills, fire ploughs, fire saws, 'thong' saws. I'm pretty sure that steel dates from post biblical times, but there were flint and steel sets from all over the world (Japan, Africa, Egypt, Peru) so it is quite possible that flint and pyrites may have been used. If you want to see an extensive collection of firemaking tools, this is well worth a visit. Adjacent cases contain cordage and woven baskets, which may be of interest to bushcrafters.
However, I'd be inclined to say that some form of drill is the most likely, given the relatively dry climate of the middle east and the fact that drill firelighting was used in ancient Egyptian times and would therefore have been known about in New Testament times. However, some of the drills were from Greenland, so a cold, damp climate does not preclude the use of friction firelighting (as many BCUK members prove on a daily basis!).
Although we bushcrafters seem to like the process of firelighting, I would have thought that when a fire forms an essential part of your life, you would generally try to ensure that the fire, or at least embers, are maintained, so that the need to go through the process of drilling for an ember is not something that you would be doing every day.
Geoff