"bound off like an arrow or a crossbow bolt" is describing their movement. bounding is a type of running usually used to describe a fast, leaping motion. the simile "like an arrow or a crossbow bolt" describes the speed of the bounding as quick because arrows and bolts are fired at high speeds from bows/crossbows. I would need more context to fully understand the second half of the sentence but "arbiters" is another word for "judges". It appears here the sentence is saying they leapt into the situation quickly thinking they were judges of right and wrong.
Hope this helps :)