Do Victor Poison-Free Insect Magnet Traps actually work on spiders?
These will generally work on hunting spiders, such as jumping, wolf and fiddleback (recluse) spiders. The hunting spiders go and look for food, and will thus be attracted to insect pheromones as they indicate the presence of a group of insects (males fighting over females and/or "orgies" of large numbers of both sexes), providing ample opportunity for the spider to nab a meal.

Web-weavers, not so much; they don't go hunting for their meals, instead waiting for the food to come to them. So, the myriad web-spinner spiders including most of the big scary ones like garden spiders, orb weavers, funnel-webs and black widows, won't fall for these types of traps; really the only way to get rid of those types of spiders is a poison of some sort, which they'll get on their feet as they move around, then ingest when they clean themselves (most insect/arachnid species are rather fastidious). 

Understand that spiders are beneficial, even inside your home, though I definitely get why you don't want them hanging out in the bedroom.