The air in the shuttlebay is going to be expelled pretty much instantly
We've never seen the entire main shuttle bay of course, but if we were to go by some of the blueprints released through the years and the known size of the door, it would take several seconds to vent the atmosphere.
The mass of the air in the shuttlebay may be 6,000 tonnes but the mass of the Enterprise is around 4.5 million tonnes.
Yet the Enterprise does move sufficiently far to avoid the collision, with the shuttle bay's atmosphere as the only propulsion.
So consider, part of the impulse drive includes "space-time driver coils
" that reduces the Enteprise's mass, thus making it possible for the impulse engine's thrust to move the ship. Now from dialog the impulse engine were not producing thrust (neither were the maneuvering thrusters) , but if the driver coils themselves were still in operation, this would enable the thrust from the shuttle deck's open doors to move the Enterprise.
Again, the Enterprise does move.