If I were to hazard an educated guess, I'd say the tech's not even more advanced in basic concept, it's just a more refined and efficient iteration of the same tech we use for superluminal travel. It would be rather wasteful for our ships to use their alcubierre drives to move around at combat speeds, considering the energy requirements and mass interference we'd have to deal with. The Thargoids clearly have no such issues and can bend spacetime to their will, allowing them to forego the need for conventional thrusters, as well as likely offering additional protection against human weaponry. I'd imagine a bullet passing through a warp field probably won't come out the other side looking the same as it went in.