Presumably things fall in the shuttle bay because of Enterprise's gravity plating, but once outside the bay it's outside its influence and will simply travel in a straight line at a constant velocity. If we give it a generous fall height inside the shuttle bay of 10 meters, that's a mere 14 m/s or 32 mph.
The Enterprise isn't at warp, there's no warp bubble or relativistic concerns. It isn't maneuvering, or being knocked about. There's no significant drag. They're in the same gravitational field. Simple Newtonian momentum says the device will continue along with Enterprise, moving away at about 14 m/s. And that's what we see, it falling straight "down". In the minute between dropping the device and contacting the bridge, it will have moved less than 1km away.
Given that this is technology 900 years in the future it's odd that Enterprise doesn't go after it either for themselves, or to prevent anyone else from having it, such as the Suliban. It's very, very, very slowly (for a spaceship) drifting away from Enterprise. Instead, we never hear about it again.
Out-of-universe, this is due to the Space Is An Ocean trope. Once something is "dropped" into space it's lost just as if you dropped it in an ocean.
I'm looking for an in-universe answer. I'd like to see what we come up with. :)