I was under the impression it was just one, at least up until you jettison it from the station. Like you say, it would mean the Alien teleporting around the place a lot, but I could put that down to simple game mechanics - it'd be boring if you had predictable periods where he wasn't around every time you travelled somewhere new.
The real question that hampers the only one Drone theory is what all the other guys were doing during this time. Sitting around the Hive twiddling their thumbs?