Would there be predictable observable signatures to Alcubierre-like “warp” drive usage? Recognizing that any Alcubierre drive system requires exotic negative energy density matter that, as far as we can tell, does not exist, if somebody managed to find such stuff in the quantities necessary to fuel a working Alcubierre drive, would it have an observable signature that could be detected from afar?
I know that there is a huge energy release at the end of the trip. But I can find little information predicting what it would look like.
If there is some predictable pattern that would be detectable from a great range, then it would seem a good target to seek out. We wouldn’t have to build an Alcubierre warp drive to prove it is possible: We would just need to look for specific kinds of flashes of energy to discover that a far more advanced civilization has already figured it out. And, in so doing, discover that such a civilization exists.
 A: It's impossible to answer this sort of question because there isn't any physical theory of warp tubes. It's often said that they are solutions of general relativity, but that really means nothing more than that they're differentiable spacetime manifolds. You can feed any such manifold into the GR field equation and get out a stress-energy tensor field. The warp tube geometries always have stress-energy distributions that don't make sense, not just because of the negative energy density but also because there isn't any apparent cause-and-effect relationship between the values at different times.
Alcubierre's original warp tube appears from nowhere (a Minkowski vacuum) and disappears back into nowhere, leaving no trace that it ever existed, and this happens for no reason. You could write down a geometry in which there are gravitational waves left behind (or at least an approximation of one), but it's the same as writing a novel in which A and then B happens: there is no actual cause-and-effect connection from A to B, only from your imagination to {A,B}.
Re the "huge energy release at the end of the trip", I think this comes from treating the Alcubierre geometry as a fixed background and plotting test-particle geodesics in it. The paper that PM 2Ring linked in a comment seems to be of that type (judging by the abstract). The calculations of this sort that I've seen assume that the wall of the tube is transparent and that the tube moves in a straight line. If you wanted to avoid their conclusions, I think it's sufficient to violate either assumption, which, as with anything else in this field of research, is just a matter of saying that it's so.
A: A detection would be pretty unlikely for the foreseeable future: we would not be able to detect it unless they pass very close to us and emit a very energetic gravity wave.
Currently we are able to detect very energetic events, such as the $10^{47}$ Joule GW150914 event with a luminosity distance of 440 megaparsecs (about $10^{25} m$). It is unlikely that practical warp drives will generate such enormous energies as gravitational waves, but even considering the solar system edge (about $10^{13} m$) the warp drive would need to emit about $10^{26}$ Joule ($\propto r^2$) to be detectable, which is still pretty large, about the energy emitted by the sun in a second.
