Of course, planets and stars would be more like trying to push an NFL linebacker out of the way of your Cheerio...
Masses smaller than your warp bubble would be "moved" out of the way as your bubble distorts the reference space/time. Like pushing a Cheerio through a bowl of milk. It'd push the other O's aside as it passed.
Sleep training our youngest. She doesn't like sleeping in her crib and let's us know this fact several times a night...
Of course, planets and stars would be more like trying to push an NFL linebacker out of the way of your Cheerio...
If we are talking interstellar space it is uncharted space for anything smaller than star.
Considering our starship will be smaller than a great many objects that could be in our path I think traveling at greater than light speed would be extremely risky.
Planet size objects could be in our path and we would have no way of knowing and traveling a greater than light speed we would never know.
It would be an interesting equation however an object of infinite mass striking an immovable object.