But having a star or black hole directly in your path seems to be inescapable death to me at any speed.
Think of the space/time "bubble" as a gravity based version of the meniscus of the soap bubble. As the energy of the artificial vs natural space/time meet, one should react to the other. Same thing with opposing magnetic fields. The strong and more direct the interaction, the more one will over power the other. Absent that, they just kind of "slide" around each other.