A compass is useful in benchmark hunting for two purposes.
The usual use of a compass is to be able to follow the to-reach instructions to find the mark. These instructions always seem to be no more precise than an 8-point compass (N, NE, E, SE, etc.).
The other mode of compass use is in using the box score to find a main station from a reference mark or vice versa (see this article on how to do this). The box score uses the format dddmmss.s but for finding purposes, using just the ddd part generally offers sufficient precision. For the really stubborn cases, or ones that involve distances longer than 20 feet, a compass that reads to the nearest degree can be useful. They are much more expensive than the usual hand compass, however.