Alcubierre drive and inertia. What is the inertia or velocity of a vehicle upon exiting or shutting down an Alcubierre bubble?  Would the vehicle maintain the velocity it had in the bubble?
I'm not sure I asked the question in a meaningful way so I'll try another question that targets what I'm after. If a vehicle was traveling in one of these bubbles how hard would it be to come to a full stop?
 A: All the treatments of the Alcubierre drive I've seen have not dealt with the acceleration and deceleration. The nearest I've seen is the paper The Alcubierre Warp Drive: On the Matter of Matter, but this is mainly interested in the interactions of matter with the drive and it doesn't deal with the mechanism of acceleration.
You'd have to specify how the acceleration was achieved. For example it might be achieved by gradually bringing the exotic matter from infinity, or if you were using some sort of field generator as proposed by Harold White by ramping up the field. In either case there's probably no analytic solution to the equation of motion so you'd have to do it numerically.
There is probably a way to ramp up the drive that produces no inertial forces on the occupants. They would feel no force as the ship accelerates then decelerates, and with the drive off their original velocity would be unchanged. However I must emphasise that in the absence of any proper treatment of the problem no definitive statement can be made.
A: Because of the way that an Alcubierre drive alters space to get a ship to exceed $c$, unwarping that space (in order to stop/travel at sublight speeds) would undo the fancy compression/expansion of space that allows the ship to travel above $c$.  In short, the act of destroying the "warp bubble" would bring the ship's velocity down below $c$.  The ship would then travel at some high fraction of $c$ until it stopped, jumped back to warp, etc.
As to how long/hard it would take to stop, the quickest and easiest way would probably be to reverse the direction of the warp bubble.  This would stop it rather quickly (no numbers, as I doubt anyone has ever calculated anything exact), probably within a few "bubble-lengths".  The rapid "deceleration" would likely wreak havoc on the occupants of the craft though.
