Getting back out of an Alcubierre warp bubble

The interior of the bubble is causally disconnected. It's not possible for the bubble to be turned off or steered from the inside. But there is no reason it cannot be affected from an outside agency at a pre-planned points, or even simply have a finite lifetime, naturally deteriorating to stop at the intended destination.

that upon traveling to some distant star system, since you never moved through space, once you turn off the bubble, and the space behind you contracts back to its normal state and the space in front of you expands back to its normal state, you're back where you started

That is not the case. The statement "you never moved through space" just means you never move relative to the bubble interior, which is different from the bubble itself moving through space. Even if the bubble accelerates, you will not experience any g-forces.

Intuitively, one can think of it as dual to the cosmic expansion of space: as space expands, it carries galaxies along with it, and because it's space between them that's expanding rather than them moving in space, distant galaxies can have superluminal separation velocity. Effective movement because of the way space expands (or contracts) is different from movement in space.

Even if cosmic expansion could somehow be "turned off", it wouldn't suddenly make all the galaxies contract together again. It would simply stop further separation.

The Alcubierre drive does something similar: instead of expanding space to get away from from distant objects, it contracts it in order to approach them. It doesn't actually need to contract all of space in front of it; it just expands it back after traversing it. In effect, the warp bubble rides its own gravitational field.

Although Newtonian analogies are fraught with peril (esp. here, since not only is gravity different, but the behavior of negative mass especially so~don't take this seriously!), but a fun little toy exercise is to consider what would happen if you lived in a Newtonian universe and had two masses, equal in magnitude but one positive and the other negative.

Pete, please elaborate your question, the original paper by Miguel describes how one can travel back and to a destination using the warp drive. The space in front is contracted to get closer to the destination, and the space behind is expanded. For getting out of the bubble, let's use the picture below:

Warp Bubble, credits go the respective authors/artists.

The bubble is created, so to speak, through the exotic matter that one will use. So if the mechanism that creates the exotic matter to keep up the bubble has a stop button, you press it and the bubble will go away :)

Hope that helps.