I don't know if anyone other than me has watched the SyFy channel show "Dark Matter", in which a crew of misfits with induced amnesia are roaming the galaxy in a stolen spaceship trying to figure out who they are and who is chasing them. In the past season they accidentally acquired a prototype star drive they call a "blink" drive, because instead of having to plow through hyperspace, they could now instantaneously shift from one point to another in the galaxy without traversing any sort of space in between. As the PTB of their reality became aware of this game-changing capability, the efforts to find them increased exponentially.

I'm pretty sure any aliens who visit us wouldn't be using anything as primitive as the Alcubierre Drive, or even the somewhat similar Heim Drive, which probably wouldn't have the gamma-burster drawback of the Alcubierre Drive, being slightly more elegant in its physics, although the Heim Theory is the subject of much controversy.