I'm working on a novel where the characters inhabit a rogue planet. Would that planet get hit by more asteroids due to the fact that it isn't orbiting a star? I have a feeling that the distance is negligible, but I can't really find an answer to this question.
Fewer. There is very little in interstellar space. The gravitational attraction of stars pulls most of the material into stellar systems. Furthermore, it keeps it there. To be sure, the orbits and other planets may cause an asteroid to miss a planet, but it will get many chances unless its orbit takes it out of the system. Any given rogue asteroid will get one chance at any rogue planet.
It is conceivable that there might be systems where orbital dynamics protect a planet from asteroids (some scientists believe Jupiter limits the asteroids striking Earth), and some interstellar space where supernovae explosions have driven a lot of asteroids from orbits, where one given rogue planet is more likely to be hit than one given system planet, but by and large, rogue planets will get fewer.
I upvoted @Mary's answer and you should too, but I'd like to build on it.
Mary is absolutely correct that statistically a rogue planet is unlikely to be struck by an asteroid or meteor. But you've not told us where that rogue is. Is it passing through a nebula? How dense is the nebula? I can easily imagine a supernova resulting in an expanding field of gravel that was once a planet moving away from the center of the exploded star. Is it passing through that?
In other words, this is one of those rare questions that can be answered as-is without voting to close it as story-based because, as Mary says, the statistical likelihood of impact in interstellar space is, on average, whomping low.
But this question also has a story-based element in that if you want the rogue to have plentiful asteroid/meteor strikes, there are plenty of natural phenomena that rationalize that result.
It all depends on where the rogue's travels took it.